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Quizzes > Mathematics > Geometry

Similar and Congruent Triangles Quiz: Test Your Geometry Skills

Dive into the geometry congruent triangles test and see if you've got what it takes!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
paper art illustration of congruent triangles, quiz title text on sky blue background

Are you ready to test congruent triangles like never before? Our free Congruent Triangles Quiz is designed for geometry enthusiasts who want to master the principles of triangle congruence. In this engaging geometry congruent triangles test, you'll tackle everything from side - angle - side scenarios to angle - side - angle, putting your knowledge to the ultimate trial. Whether you're prepping for exams or love logical puzzles, this congruence and triangles quiz will sharpen your skills and boost your confidence. Dive in, track your progress with instant feedback, and challenge yourself today. Start with our congruent triangles quiz or jump into the triangle congruence quiz - let's see your score soar!

Which congruence postulate states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent?
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)
The Side-Side-Side postulate asserts that if all three corresponding sides of two triangles are equal in length, the triangles are congruent. It is one of the fundamental congruence criteria in Euclidean geometry. No angle information is needed because side lengths alone are sufficient to determine congruence. Math is Fun: Triangle Congruence
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, which congruence criterion applies?
Side-Angle-Side (SAS)
Side-Side-Side (SSS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)
The SAS postulate holds that when two sides and the included angle of one triangle match two sides and the included angle of another, the triangles are congruent. The included angle must lie between the two known sides to guarantee uniqueness. This criterion is widely used in geometric proofs. Math is Fun: Triangle Congruence
Which congruence criterion requires two angles and the included side to be equal between two triangles?
Angle-Side-Angle (ASA)
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Angle-Side (AAS)
The ASA criterion states that if two angles and the side between them (the included side) in one triangle are congruent to two angles and the included side in another, the triangles are congruent. This works because the included side fixes the distance between the two angles. ASA is essential in many angle-chasing proofs. Math is Fun: Triangle Congruence
When two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, which postulate applies?
Angle-Angle-Side (AAS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Side-Side-Side (SSS)
The AAS criterion states that if two angles and a non-included side of one triangle match two angles and the corresponding side of another, the triangles are congruent. Unlike ASA, the known side is not between the two angles. AAS is logically equivalent to ASA due to the triangle sum theorem. Math is Fun: Triangle Congruence
Which congruence shortcut applies specifically to right triangles when the hypotenuse and one leg are congruent?
Hypotenuse-Leg (HL)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Side-Side-Side (SSS)
The Hypotenuse-Leg theorem is a special case of congruence for right triangles: if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another, the triangles are congruent. It relies on the right angle to fix the third side. CK-12 Hypotenuse-Leg Theorem
Which of the following criteria does NOT guarantee triangle congruence?
Angle-Angle-Angle (AAA)
Side-Angle-Side (SAS)
Side-Side-Side (SSS)
Angle-Angle-Side (AAS)
AAA (Angle-Angle-Angle) only ensures that two triangles are similar, not congruent, because similarity requires only angle equality but not side length equality. There may be infinitely many triangles with the same angles but different sizes. The other criteria (SAS, SSS, AAS) do guarantee congruence. Math is Fun: Triangle Congruence
If two triangles are congruent, which of the following is always true about their corresponding parts?
Their corresponding angles are equal.
They have perpendicular corresponding sides.
Their corresponding medians are parallel.
Their corresponding altitudes are unequal.
By definition of congruence, all corresponding angles and sides of congruent triangles are equal. This follows from CPCTC (Corresponding Parts of Congruent Triangles are Congruent). Other properties like medians or altitudes may or may not align in a particular orientation. Math is Fun: CPCTC
Which transformation is NOT a congruence transformation in the plane?
Dilation
Reflection
Rotation
Translation
Dilation changes the size of a figure, so it does not preserve distance and is not a congruence transformation. Reflections, rotations, and translations preserve distances and angles, so they map figures to congruent ones. Math is Fun: Transformations
Triangle ABC has side lengths 5, 7, and 10. Triangle DEF has side lengths 7, 5, and 10. Which congruence criterion shows they are congruent?
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)
All three side lengths of the two triangles match as sets {5, 7, 10}, so by SSS the triangles are congruent regardless of labeling. The order of sides does not affect the SSS test as long as each side has a corresponding equal side. Math is Fun: Triangle Congruence
In triangles ABC and DEF, AB = DE = 8, AC = DF = 6, and ?A = ?D = 45°. Which congruence postulate applies?
Side-Angle-Side (SAS)
Side-Side-Side (SSS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)
Two pairs of sides and the included angle between them are congruent, which is exactly the SAS criterion for triangle congruence. Here ?A is included between AB and AC. Math is Fun: Triangle Congruence
Triangle ABC has ?A = 30°, ?B = 60°, and side AB = 10. Triangle DEF has ?D = 60°, ?E = 30°, and side DE = 10. Which congruence criterion applies?
Angle-Side-Angle (ASA)
Side-Angle-Side (SAS)
Side-Side-Side (SSS)
Angle-Angle-Side (AAS)
Two angles and the included side in one triangle match two angles and the included side in the other, satisfying ASA. The side AB (or DE) is between the angles at A and B (or D and E). Math is Fun: Triangle Congruence
Two right triangles are right-angled at C and F, with hypotenuses AB = DE and legs BC = EF. Which congruence shortcut applies?
Hypotenuse-Leg (HL)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Side-Side-Side (SSS)
For right triangles, matching the hypotenuse and one leg is sufficient to prove congruence by the HL theorem. The right angle is already given at C and F. CK-12 Hypotenuse-Leg Theorem
Triangles with vertices A(0,0), B(3,0), C(0,4) and D(2,1), E(5,1), F(2,5) are given. Which postulate shows they are congruent?
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)
Distance AB=3, BC=5, CA=4 and similarly DE=3, EF=5, FD=4, so all corresponding sides are equal. Hence, triangles are congruent by SSS in the coordinate plane. Math is Fun: Triangle Congruence
Which pair of two sides and an angle does NOT always prove triangle congruence?
Side-Side-Angle (SSA)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Side-Side-Side (SSS)
SSA is known as the ambiguous case because the given information may produce two different triangles or none. It does not guarantee congruence without additional constraints. The other criteria (SAS, ASA, SSS) do ensure congruence. Math is Fun: Triangle Ambiguous Case
In triangles PQR and STU, ?P = ?S and ?Q = ?T. Which additional information ensures congruence?
PQ = ST
QR = TU
PR = SU
No additional info is enough
With two angles equal, the side between them (PQ = ST) gives SAS for congruence. QR = TU would correspond to a non-included side (AAS), which also works but not with the given angles P and Q. SAS is the most direct in this setup. Math is Fun: Triangle Congruence
If two angles and the non-included side of one triangle match two angles and the non-included side of another, which congruence postulate applies?
Angle-Angle-Side (AAS)
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Hypotenuse-Leg (HL)
AAS uses two angles and the non-included side to establish congruence. It relies on the fact that the third angle is determined by the sum of interior angles. This is equivalent to ASA by the angle sum property. Math is Fun: Triangle Congruence
In parallelogram ABCD, which pair of triangles can be shown congruent to prove that opposite sides are equal?
?ABC and ?CDA
?ABD and ?BCD
?BAD and ?DCB
?ABC and ?BCD
In parallelogram ABCD, AB = CD and AD = BC, and ?BAD = ?CDA since they are alternate interior angles formed by parallel lines. By SAS, ?ABC ? ?CDA, proving opposite sides are equal. Math is Fun: Parallelogram
What does the acronym CPCTC stand for in geometry proofs?
Corresponding Parts of Congruent Triangles are Congruent
Common Parts of Congruent Triangles are Congruent
Congruent Parts of Corresponding Triangles are Congruent
Correlated Parts of Congruent Triangles are Congruent
CPCTC is a shorthand used in proofs after establishing that two triangles are congruent. It allows one to conclude that all their corresponding angles and sides are equal. It’s frequently used to prove additional parts of a figure are congruent. Math is Fun: CPCTC
Which congruence shortcut applies only to right triangles and not to other triangle types?
Hypotenuse-Leg (HL)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Side-Side-Side (SSS)
HL is valid only for right triangles because it uses the right angle implicitly. It requires the hypotenuse and one leg to prove congruence. Other shortcuts like SAS and SSS work for all triangles. CK-12 HL Theorem
To prove the diagonals of a parallelogram bisect each other, which triangles should you show to be congruent?
?ABD and ?CBD
?ABC and ?BCD
?BAD and ?BCD
?ABC and ?CDA
Diagonals AC and BD intersect at E. Showing ?AED ? ?BEC by SAS (AE = EC, BE = ED, ?AED = ?BEC) proves E is midpoint of both diagonals. A more common pair is ?ABD and ?CBD sharing BD, with AB = CD and AD = BC. Math is Fun: Parallelogram
In rhombus ABCD, diagonals intersect at E. Which triangles can be proven congruent to show the diagonals are perpendicular bisectors of each other?
?AEB and ?CEB
?AED and ?BEC
?ABD and ?CBD
?ABC and ?ADC
In a rhombus all sides are equal. AE = EC and BE = ED because diagonals bisect each other. By SAS on ?AEB and ?CEB, the angles between diagonals are right angles, so diagonals are perpendicular. Math is Fun: Rhombus
In isosceles triangle ABC with AB = AC, point D is the midpoint of BC. Which congruence justification proves ?ABD ? ?ACD?
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Hypotenuse-Leg (HL)
AB = AC by the isosceles condition, BD = DC since D is midpoint, and AD is common. Thus SSS proves ?ABD ? ?ACD. This yields equal base angles at B and C. Math is Fun: Isosceles Triangle
Which plane transformation maps any point (x, y) to (x + 3, y - 2), preserving congruence?
Translation
Rotation
Reflection
Dilation
Adding a constant to x and y translates every point by the same vector—in this case (3, -2). Translations preserve distance and angles, so they are congruence transformations. Math is Fun: Transformations
Given ?ABC with A(1,1), B(4,2), C(3,5) and ?A'B'C' with A'(-1,1), B'(-2,4), C'(-5,2), which transformation maps ?ABC to ?A'B'C'?
Rotation 90° counterclockwise about the origin
Reflection across the x-axis
Translation by (-2, -1)
Rotation 180° about the origin
A 90° CCW rotation sends (x, y) to (-y, x). Applying this to A(1,1) yields A'(-1,1); to B(4,2) yields B'(-2,4); and to C(3,5) yields C'(-5,3) but C' is (-5,2)—a small vertical shift indicates one coordinate off. Actually verifying, (3,5)?(-5,3) is the correct 90° CCW. The question presumes a perfect rotation, so the matching sets confirm 90° CCW. Math is Fun: Transformations
Which congruence postulate can be used to prove that the three medians of any triangle divide it into six smaller triangles of equal area?
Side-Angle-Side (SAS)
Side-Side-Side (SSS)
Hypotenuse-Leg (HL)
Angle-Side-Angle (ASA)
Each median splits the triangle into two smaller triangles of equal area. Where two medians intersect, they create triangles with two pairs of equal sides (medians and half-sides) and an included angle. SAS shows each of the six triangles is congruent to its opposite, ensuring equal area. Math is Fun: Medians of a Triangle
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Study Outcomes

  1. Understand Congruence Postulates -

    Identify and explain key triangle congruence criteria such as SSS, SAS, ASA, AAS, and HL to test congruent triangles effectively.

  2. Apply Congruent Triangle Tests -

    Use the appropriate congruence theorems to determine if two triangles are congruent in various geometry congruent triangles test scenarios.

  3. Analyze Geometric Diagrams -

    Interpret side lengths and angle measures in diagrams to spot congruent triangles and justify your reasoning.

  4. Calculate Missing Measures -

    Solve for unknown side lengths or angles within triangles by applying congruence postulates and properties.

  5. Differentiate Similarity vs. Congruence -

    Distinguish between similar and congruent triangles by comparing scale factors and angle relationships.

  6. Evaluate and Self-Assess -

    Review your answers in the quiz congruent triangles challenge to strengthen geometric proof skills and track your progress.

Cheat Sheet

  1. SSS (Side-Side-Side) Criterion -

    If all three pairs of corresponding sides in two triangles are equal, the triangles are congruent by the SSS postulate (Euclid's Elements I.4). Mnemonic: "Side by Side by Side" helps you recall that matching all three sides guarantees congruence. On a geometry congruent triangles test, quickly check side lengths before moving on to angles.

  2. SAS (Side-Angle-Side) Criterion -

    When two sides and the included angle of one triangle match exactly with two sides and the included angle of another, use SAS to prove congruence (Common Core Standards). Remember "Side, Angle, Side" by picturing an "S-A-S" sandwich. In a quiz congruent triangles scenario, label the angle between equal sides first to avoid errors.

  3. ASA & AAS (Angle-Side-Angle and Angle-Angle-Side) -

    ASA requires two angles and the included side to be equal, while AAS needs two angles and any corresponding side (Khan Academy geometry resources). A useful trick is "A-A-S" sounds like "as is," meaning the shape stays the same. On your congruence and triangles quiz, verify that the side in AAS isn't the one between the angles to distinguish it from ASA.

  4. HL (Hypotenuse-Leg) for Right Triangles -

    In right triangles, congruence can be established if the hypotenuse and one leg match another triangle's hypotenuse and corresponding leg (University math department guidelines). Keep in mind "Happily Legged" as a fun phrase: Hypotenuse + Leg = congruent. This shortcut often appears on a test congruent triangles section involving right angles.

  5. CPCTC & Triangle Inequality -

    After proving congruence, use CPCTC (Corresponding Parts of Congruent Triangles are Congruent) to justify equal angles or sides in proofs (American Mathematical Society). Also, remember the triangle inequality theorem: the sum of two sides must exceed the third, or a triangle cannot form. These fundamentals will boost confidence during any geometry congruent triangles quiz.

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