Question

Prove the congruency between two triangles using two sides and a median drawn to one of them

Answer 1

To prove congruency between two triangles using two sides and a median drawn to one of them, we can use the Side-Side-Side (SSS) congruency criterion.

Step-by-step explanation:

To prove congruency between two triangles using two sides and a median drawn to one of them, we can use the Side-Side-Side (SSS) congruency criterion.

Here are the steps:

1. Given: Triangle ABC and triangle XYZ, where AB = XY, BC = YZ, and median CD is drawn to triangle ABC.
2. Show that angle BAC = angle XYZ.
3. Since CD is the median, it divides AB into two equal segments, AD and DB. Therefore, AD = DB.
4. By SSS congruency criterion, triangle ACD is congruent to triangle XDY. So, angle ACD = angle XDY.
5. Since AD = DB, triangle BCD is congruent to triangle YDZ by SSS. So, angle BCD = angle YDZ.
6. Therefore, angle BAC = angle XYZ (Alternate Interior Angles).
7. By Angle-Angle (AA) congruency criterion, triangle ABC is congruent to triangle XYZ.