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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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.
