Question

Please help with this

Answer 1

Explanation:

The note "SAS Congruence" under the middle box tells you this proof will be accomplished by showing two sides and the included angle are congruent. (That's what S A S refers to.)

One of the angles is shown in the upper left box as ∠TMI. The note under that box tells you the other angle is a vertical angle with ∠TMI. By referring to the diagram, you see that the vertical angle is ∠EMR.

The middle box on the left and the bottom box on the left share the note "M is a midpoint." This tells you the segments of interest are the congruent segments of which M is the midpoint. The Given information tells you M is the midpoint of ET and of RI. The middle left box is already filled with TM ≅ EM, so the bottom box needs to be filled with the letters of the other segments: RM ≅ IM.

The three congruence relationships on the left, involving an angle and two  sides either side of that angle mean that you can invoke the SAS Congruence theorem to say ΔTMI ≅ ΔEMR. Be sure to write the triangle names so that T corresponds to E, and I corresponds to R. This is the relation that goes in the middle box.

The right side box is the desired conclusion, the whole point of the proof: ∠T ≅ ∠E. The corresponding note is "CPCTC" (corresponding parts of congruent triangles are congruent).