Geometry Test Review Practice Quiz

The sum of the interior angles of a triangle is always 180 degrees. This fundamental property of triangles is a cornerstone in Euclidean geometry and is frequently used in solving geometric problems.

A right angle is defined as having a measure of 90 degrees. This is an essential definition in geometry used to determine perpendicularity and many other properties of shapes.

In a rectangle, opposite sides are both equal and parallel. This property distinguishes rectangles from other quadrilaterals where these conditions may not hold.

By definition, the diameter of a circle is twice as long as its radius. This relationship is critical for solving problems involving circles and their properties.

A square is defined as a quadrilateral with four congruent sides and four right angles. This unique set of properties distinguishes it from other quadrilaterals like rectangles and rhombi.

The area of a circle is given by the formula A = πr², which is fundamental to circle geometry. This formula should not be confused with the formula for circumference.

The circumference, which is the distance around the circle, is calculated using C = 2πr. This distinguishes it from the area formula and is critical for many circle-based problems.

Using the Pythagorean theorem, 3² + 4² equals 9 + 16, which is 25, so the hypotenuse is the square root of 25, namely 5. This theorem is a key concept in right triangle geometry.

The midpoint is calculated by averaging the corresponding coordinates, so ((2+8)/2, (3+7)/2) results in (5, 5). This concept is essential in coordinate geometry.

The equation is in vertex form, y = (x - h)² + k, so the vertex is exactly (h, k), which in this case is (3, 2). Recognizing this form simplifies identifying the vertex of a parabola.

Adjacent angles in a parallelogram are supplementary, meaning they add up to 180°. Therefore, if one angle is 70°, the adjacent angle must be 110°.

A unique property of rectangles is that their diagonals are congruent, which is not generally true for all parallelograms. This feature helps in distinguishing rectangles from other quadrilaterals.

The intercepted arc corresponds to the fraction of the circle equal to the central angle divided by 360°. Here, 60°/360° simplifies to 1/6.

The volume of a cube is found by raising its side length to the third power, i.e., s³. This formula is a fundamental concept in three-dimensional geometry.

The Pythagorean Theorem is a central principle in geometry that relates the sides of a right triangle. It confirms that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

For an inscribed circle, the diameter is equal to the side length of the square, making the radius half of that length (5 units). Using the area formula A = πr², the area computes to 25π.

In similar figures, the ratio of the areas is the square of the ratio of the corresponding sides. Here, (5/2)² equals 25/4, and multiplying 8 by 25/4 results in an area of 50.

A regular hexagon has six lines of symmetry due to its equal sides and angles. These symmetries include lines drawn through opposite vertices and through the midpoints of opposite sides.

The standard form of a circle's equation is (x - h)² + (y - k)² = r². In this equation, h is 4, k is -3, and r² is 49, so the radius is 7.

Since 7² + 24² equals 25², the triangle satisfies the Pythagorean Theorem and is therefore a right triangle. This set of side lengths is a classic example of a Pythagorean triple.