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

Draw a perpendicular from P to AB. Label the intersection C. We are given that PA = PB, so PA ≅ PB by the definition of congruent _______ lines. We know that angles PCA and PCB are right angles by the definition of _________ lines right angle. PC ≅ PC by the definition of ________ _________ property. 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.

1) congruent segments 2)perpendicular lines 3)reflexive proterty 4)CPCTC

Which pair of triangles can be proven congruent by the HL theorem?

Option 2

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

Since these are right triangles, the unmarked sides can be determined to be congruent because of the Pythagorean theorem. Once the third set of congruent sides is determined, the SSS or SAS theorem can be used to prove triangle congruency.

Could these triangles be congruent?

no, because the hypotenuses must have different lengths

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

A. translation, then rotation, then reflection

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

A. x = 3, y = 11