Question

Copy the problems onto your paper, mark the givens and prove the statements asked.

Given ∠E ≅ ∠T, M − midpoint of TE Prove: MI ≅ MR

Answer 1

MI ≅ MR proved by using ASA postulate of congruence

Step-by-step explanation:

Let us revise the cases of congruence

• SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ  
• SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ  
• ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ  
• AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ  
• HL ⇒ hypotenuse leg of the 1st right Δ ≅ hypotenuse leg of the 2nd right Δ  

∵ M is the mid-point of TE

∴ MT = ME

In Δs TMI and EMR

∵ ∠T ≅ ∠E ⇒ given

∵ ∠TMI ≅ EMR ⇒ vertical opposite angles

∵ MT = ME ⇒ proved

∴ Δ TMI ≅ ΔEMR by ASA postulate of congruence

- From congruence, corresponding sides are equal

∴ MI ≅ MR

MI ≅ MR proved by using ASA postulate of congruence

Learn more;

You can learn more about the cases of congruence in brainly.com/question/6108628

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