Week 5: Proving and Applying the SAS and SSS Congruence Criteria

Question 1

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

Revolt · Accepted Answer

translation, then rotation, then reflection

Question 2

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.

Question 3

Complete the missing parts of the paragraph proof.

Revolt · Accepted Answer

congruent segments; 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 ≅ P: congruent segments; 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 ≅ P: perpendicular lines; 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 ≅ P: reflexive property; 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 ≅ P: CPCTC

Question 4

bisector✔ perpendicular lines right angle

Revolt · Accepted Answer

✔ perpendicular lines

Question 5

definition of congruent✔ reflexive propertysubstitution property

Revolt · Accepted Answer

✔ reflexive property

Question 6

SASASA✔ CPCTC

Revolt · Accepted Answer

✔ CPCTC

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

Make a conjecture about the diagram below. Do you think you can conclude that △JKL ≅ △XYZ? Explain your reasoning.

Revolt · Accepted Answer

Make a conjecture about the diagram below. Do you think you can conclude that △JKL ≅ △XYZ? Explain your reasoning.

Question 9

Could these triangles be congruent?

Revolt · Accepted Answer

no, because the hypotenuses must have different lengths

Question 10

Complete the missing parts of the paragraph proof.

Revolt · Accepted Answer

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 ≅ P: congruent segments; 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 ≅ P: perpendicular lines; 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 ≅ P: reflexive property; 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 ≅ P: CPCTC

Week 5: Proving and Applying the SAS and SSS Congruence Criteria Answers

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