Middle School

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

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

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 :

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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Rewritten by : Barada

Final answer:

The question is about a geometry proof related to congruent angles and midpoints, but additional information is needed to provide a specific solution.

Explanation:

The question appears to be a geometry proof involving congruent angles and midpoints. The goal is to prove that two line segments MI and MR are congruent given ∠E ≅ ∠T, and M is the midpoint of TE.

To prove this, one would need to provide more information about the points I and R, such as their positions relative to point E, T, and M.

Without this additional information, it is difficult to give a specific proof. However, typical proof strategies might involve showing that triangles EMI and TMR are congruent by Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS) postulates, depending on the position of points I and R.