If two altitudes of a triangle are congruent, then the triangle is isosceles.

If two altitudes of a triangle are congruent, then the triangle is isosceles.

If two altitudes of a triangle are congruent, then the triangle is isosceles.

If two altitudes of a triangle are congruent, then the triangle is isosceles.

A

B C

D E

If two altitudes of a triangle are congruent, then the triangle is isosceles.

A

B C

D E

Given: CD and BE are altitudesto AB and AC of ABC.CD BE

Prove: ABC is isosceles.

~=

If two altitudes of a triangle are congruent, then the triangle is isosceles.

A

B C

D E

Given: CD and BE are altitudesto AB and AC of ABC.CD BE

Prove: ABC is isosceles.

~=

Given:

CD BE

Prove:

~=

The medians of a triangle are congruent if the triangle is equilateral.

The medians of a triangle are congruent if the triangle is equilateral.

The medians of a triangle are congruent if the triangle is equilateral.

The medians of a triangle are congruent if the triangle is equilateral.

A

B C

D E

F

The medians of a triangle are congruent if the triangle is equilateral.

A

B C

D E

Given:

Prove:

Given:

Prove:

F

The medians of a triangle are congruent if the triangle is equilateral.

A

B C

D E

Given: AF, BE, and CD are all medians of equilateral ABC

Prove:

Given:

Prove:

F

The medians of a triangle are congruent if the triangle is equilateral.

A

B C

D E

Given: AF, BE, and CD are all medians of equilateral ABC

Prove:

Given:

Prove:

F

The medians of a triangle are congruent if the triangle is equilateral.

A

B C

D E

Given: AF, BE, and CD are all medians of equilateral ABC

Prove:

Given: D is midpoint of AB F is midpoint of BC E is midpoint of AC

Prove:

F

The medians of a triangle are congruent if the triangle is equilateral.

A

B C

D E

Given: AF, BE, and CD are all medians of equilateral ABC

Prove:

Given: D is midpoint of AB F is midpoint of BC E is midpoint of AC

Prove:

F

The medians of a triangle are congruent if the triangle is equilateral.

A

B C

D E

Given: AF, BE, and CD are all medians of equilateral ABC

Prove:

Given: D is midpoint of AB F is midpoint of BC E is midpoint of AC

Prove:

F

The altitude to the base of an isosceles triangle bisects the vertex angle.

The altitude to the base of an isosceles triangle bisects the vertex angle.

Given:

Prove:

Given: Prove:

The altitude to the base of an isosceles triangle bisects the vertex angle.

Given:

Prove:

Given: Prove:

The altitude to the base of an isosceles triangle bisects the vertex angle.

A

B C

Given:

Prove:

D

Given: Prove:

The altitude to the base of an isosceles triangle bisects the vertex angle.

A

B C

Given: Isosceles ABC with vertex BAC and

altitude AD to side BC Prove:

D

Given: Prove:

The altitude to the base of an isosceles triangle bisects the vertex angle.

A

B C

Given: Isosceles ABC with vertex BAC and

altitude AD to side BC Prove: AD bisects BAC

D

Given: Prove:

The altitude to the base of an isosceles triangle bisects the vertex angle.

A

B C

Given: Isosceles ABC with vertex BAC and

altitude AD to side BC Prove: AD bisects BAC

D

Given: Prove:

The altitude to the base of an isosceles triangle bisects the vertex angle.

A

B C

Given: Isosceles ABC with vertex BAC and

altitude AD to side BC Prove: AD bisects BAC

D

Given: Prove:

The altitude to the base of an isosceles triangle bisects the vertex angle.

A

B C

Given: Isosceles ABC with vertex BAC and

altitude AD to side BC Prove: AD bisects BAC

D

Given: Prove: BAD CAD ~=

If two angles of one triangle are congruent to two angles of another triangle, the remaining

pair of angles are also congruent.

If two angles of one triangle are congruent to two angles of another triangle, the remaining

pair of angles are also congruent.

If two angles of one triangle are congruent to two angles of another triangle, the remaining

pair of angles are also congruent.

If two angles of one triangle are congruent to two angles of another triangle, the remaining

pair of angles are also congruent.

A

B

CD

FE

If two angles of one triangle are congruent to two angles of another triangle, the remaining

pair of angles are also congruent.

A

B

CD

FE

If two angles of one triangle are congruent to two angles of another triangle, the remaining

pair of angles are also congruent.

A

B

CD

FE

If two angles of one triangle are congruent to two angles of another triangle, the remaining

pair of angles are also congruent.

A

B

CD

Given: Prove:

FE

If two angles of one triangle are congruent to two angles of another triangle, the remaining

pair of angles are also congruent.

A

B

CD

Given: Prove:

FE

If two angles of one triangle are congruent to two angles of another triangle, the remaining

pair of angles are also congruent.

A

B

CD

Given: Prove:

FE

In this lesson we drew diagrams for problems presented

with words.