Prove that Triangle MJD is congruent to triangle TED

Question

The given Image and the required = https://imgpile.com/i/9PpurS

Answer 1

Hi Ref,

Here are some ways triangles can be proven congruent. Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), Hypotenuse-Leg (HL).

To approach the problem. Look at what information you are given and see how it can be used to prove the congruency.

The approach I would take to proving congruency is this.

1. TE and JM are parallel lines, JE is a transversal. ∠TED and ∠MJT are congruent. Alternate interior angles of a transversal are congruent
2. ∠TDE and ∠MDJ are vertical angles so they are congruent.
3. Use Angle Side Angle to prove congruency.

Two Column Proof

MJ || TE Given

JD ≅ ED Given

∠TED ≅ ∠MJD If a transversal intersects || lines, alternate interior angles are congruent.

∠TDE ≅ ∠MDJ Vertical angles are congruent

ΔMJD ≅ ΔTED Angle Side Angle proves congruency

Hope this helps

Please let me know if you need more clarification :)