Geometry Concepts: CPCTC, Isosceles & Equilateral Theorems

The video tutorial covers various methods to prove triangle congruence, including side-side-side, side-angle-side, angle-side-angle, and hypotenuse-leg theorems. It also solves problems involving isosceles triangles and demonstrates the use of flowchart proofs. Key concepts include congruent triangles, postulates, and the properties of isosceles triangles.

Which postulate is used to prove that both triangles are congruent when given a side, an angle, and another side?

• Angle-Angle-Side

• Side-Angle-Side

• Angle-Side-Angle

• Side-Side-Side

If the legs of an isosceles triangle are x + 1 and x + 7, and the base is 3x - 3, what is the length of the base?

• 3 units

• 6 units

• 9 units

• 12 units

For the HL theorem to be applicable, what must be true about the hypotenuse and legs of the triangles?

• Neither the hypotenuse nor the legs need to be congruent

• Only the hypotenuse must be congruent

• Only the legs must be congruent

• Both the hypotenuse and legs must be congruent

Which postulate can be used to prove triangle pqr congruent to triangle sqr when RQ is a perpendicular bisector of PS?

• Side-Side-Side

• Side-Angle-Side

• Angle-Angle-Side

• Angle-Side-Angle

What property is used when adding the same segment to both sides of an equation in a proof?

• Subtraction Property

• Division Property

• Addition Property

• Multiplication Property

Which theorem states that the opposite sides of an isosceles triangle are congruent?

• Pythagorean Theorem

• Side-Angle-Side Theorem

• Isosceles Triangle Theorem

• Angle-Side-Angle Theorem

If the base angles of an isosceles triangle are 46°, what is the measure of the third angle?

• 92°

• 180°

• 88°

• 44°

What is the measure of angle X if the sum of angles in a triangle is 180° and the other two angles are 44° and 46°?

• 180°

• 90°

• 46°

• 44°

Which property states that a segment is congruent to itself?

• Reflexive Property

• Substitution Property

• Symmetric Property

• Transitive Property

What is the value of X if 2X + 38 = 180 in an isosceles triangle?

• 74

• 73

• 72

• 71