Geometry - Proofs continued

This video tutorial covers the use of postulates and theorems to prove triangle congruence, including side-side-side, side-angle-side, and angle-side-angle postulates. It explains how congruent triangles can be used to prove parallel lines and explores the properties of isosceles and right triangles. The video also introduces the hypotenuse-leg theorem for right triangles and discusses the classification of triangles by their sides and angles.

What is the significance of corresponding parts of congruent triangles?

• They are only applicable to right triangles.

• They help in proving triangles are similar.

• They allow us to conclude that corresponding angles and sides are congruent.

• They are used to calculate the area of triangles.

Which postulate is used when three pairs of sides of two triangles are congruent?

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

• Angle-Angle-Side (AAS)

How can proving triangles congruent help in determining parallel lines?

• By using the Pythagorean theorem.

• By calculating the slope of the lines.

• By establishing congruent alternate interior angles.

• By using the reflexive property.

What is a key property of an isosceles triangle?

• It has one right angle.

• It has two congruent sides and two congruent base angles.

• It has three congruent sides.

• It has no congruent sides.

Why is the reflexive property useful in triangle congruence proofs?

• It is used to calculate the perimeter of triangles.

• It is only applicable to isosceles triangles.

• It allows us to state that a side is congruent to itself.

• It helps in proving angles are equal.

What does the angle-angle-side (AAS) theorem state?

• Two triangles are congruent if they have a right angle.

• Two triangles are congruent if all three sides are congruent.

• Two triangles are congruent if two angles and a non-included side are congruent.

• Two triangles are congruent if two angles and the included side are congruent.

Why is there no side-side-angle (SSA) theorem?

• It only applies to right triangles.

• It does not guarantee triangle congruence.

• It is the same as the hypotenuse-leg theorem.

• It is used for calculating angles.

What is the hypotenuse-leg (HL) theorem used for?

• Proving congruence of scalene triangles.

• Proving congruence of obtuse triangles.

• Proving congruence of isosceles triangles.

• Proving congruence of right triangles.

Which of the following is NOT a way to classify triangles by their sides?

• Equilateral

• Isosceles

• Scalene

• Right

What is the longest side of a right triangle called?

• Leg

• Hypotenuse

• Base

• Vertex