1. ABC is an isosceles triangle. BH is median from B (i.e. H is the midpoint of AC.

a) Find two congruent triangles. Show the test.

2. ABC is an isosceles triangle (AB=BC). BH is the bisector of angle ABC. H is on AC.

a) Find two congruent triangles. Show the test.

Relevance

An icoseles triangle has 2 equal sides and 2 equal angles by definition

1.

You are bisecting the third angle, since the point H divides the line AC in 2 and AH = HC

You have 2 equal sides AB = BC, and AH = HC and a third shared side BH so you have Side Side Side

You also have equal angles BAH = BCH so you can use Side Angle Side too

2.

You have a common side, BH in both triangles

You have AB = BC so you have 2 common sides

Since ABC was bisected, you have 2 equal angles ABH and HBC so you have Side Angle Side again

We know from 1 that AH = HC too so you can use Side Side Side

You have ACB = CAB so you can use Angle Side Angle

• Anonymous

Triangle BAH is congruent to Triangle BDH by SSS. ----------------> or SAS

1. Assumption: AB and BD are the two congruent sides of the isosceles triangle, That is one pair of congruent sides.

The median BH is shared by both triangles and is congruent to itself by the reflexive property.

AH = HD by definition of median

Triangle BAH is congruent to Triangle BDH by SSS. ----------------> or ASA since angles C and A are congruent by the Isosceles Triangle Theorem

SAS could also be given because Angles A and D are congruent by the Isosceles Triangle theorem.

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Triangle BCH is congruent to Triangle B AH by SAS or ASA.

Sides BC and AB are congruent as given.

The angle bisector, Ray BH bisects angle CBA creating two smaller congrent angles, Angle CBH and Angle ABH.

The two triangles share side BH by the reflexive property, those sides are congruent.