Triangle Congruence: SSS and HL

Question 1

Draw a perpendicular from P to AB. Label the intersection C. We are given that PA = PB, so PA ≅ PB by the definition of . We know that angles PCA and PCB are right angles by the definition of . PC ≅ PC by the . So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by . Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of perpendicular bisector.

Revolt · Accepted Answer

perpendicular lines

Question 2

Draw a perpendicular from P to AB. Label the intersection C. We are given that PA = PB, so PA ≅ PB by the definition of . We know that angles PCA and PCB are right angles by the definition of . PC ≅ PC by the . So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by . Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of perpendicular bisector.

Revolt · Accepted Answer

reflexive property

Question 3

Draw a perpendicular from P to AB. Label the intersection C. We are given that PA = PB, so PA ≅ PB by the definition of . We know that angles PCA and PCB are right angles by the definition of . PC ≅ PC by the . So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by . Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of perpendicular bisector.

Revolt · Accepted Answer

CPCTC

Question 4

Could these triangles be congruent?

Revolt · Accepted Answer

no, because the hypotenuses must have different lengths

Question 5

Draw a perpendicular from P to AB. Label the intersection C. We are given that PA = PB, so PA ≅ PB by the definition of . We know that angles PCA and PCB are right angles by the definition of . PC ≅ PC by the . So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by . Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of perpendicular bisector.

Revolt · Accepted Answer

congruent segments

Question 6

The SSS proof used the rigid transformations illustrated here. Which transformations are used?

Revolt · Accepted Answer

translation, then rotation, then reflection

Question 7

Which of the following pairs of values for x and y would justify the claim that the two triangles are congruent?

Revolt · Accepted Answer

x = 3, y = 11

Question 8

What did you include in your response? Check all that apply.

Revolt · Accepted Answer

The Pythagorean theorem says that the third sides are congruent.; The Pythagorean theorem and SSS prove that the triangles are congruent.; The Pythagorean theorem and SAS prove that the triangles are congruent.

Triangle Congruence: SSS and HL Answers

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