Final Exam - Triangles and Transformations

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².

Front

How do you find the length of a side in a right triangle using the Pythagorean Theorem?

Back

To find the length of a side, rearrange the Pythagorean Theorem formula. For example, to find side a: a = √(c² - b²).

Front

What happens to the coordinates of a point when it is reflected across the x-axis?

Back

When a point (x, y) is reflected across the x-axis, its new coordinates become (x, -y).

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

Can a triangle have sides of lengths 3, 4, and 9?

Back

No, because 3 + 4 is not greater than 9, violating the Triangle Inequality Theorem.

Front

What does it mean for triangles to be congruent?

Back

Triangles are congruent if they have the same size and shape, which can be proven using criteria such as SSS, SAS, ASA, AAS, or HL.

Front

What is the difference between similar and congruent triangles?

Back

Similar triangles have the same shape but not necessarily the same size (corresponding angles are equal, and sides are proportional). Congruent triangles are identical in size and shape.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and a non-included side are known.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle are known.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side are known.