Wednesday, November 9, 2016

Tuesday, November 8, 2016

The bisector of the vertex angle of an isosceles triangle separates the triangle into two congruent triangles


The bisector of the vertex angle of an isosceles triangle separates the triangle into two congruent triangles
 Bisector of the vertex angle of an isosceles triangle
Given
Isosceles triangle ABC with AB = AC
AO bisects ,


Prove


Proof

1: AB=AC - Given
2: - Given

3: AO = AO - Identity

- From 1,2,3 - If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent (SAS)

Sunday, November 6, 2016

If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the triangles are congruent (AAS)

Given
If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the triangles are congruent (AAS)
Triangles ABC, EFG



AC = EG

Prove
 


Proof
1:
- Given
2: - From 1  - If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent

3: AC = EG - Given

4: - From 1,2,3 - If two angles  and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent (ASA).

Friday, November 4, 2016

Corresponding altitudes of congruent triangles are congruent

Corresponding altitudes of congruent triangles are congruent
Given:


Altitudes CD to AB and TV to RS

Prove
CD = TV








Proof
1: AC = RT - correosponding sides in congruent triangles ( ) are equal

2: - correosponding angles in congruent triangles () are equal

3:  - Given (Altitudes CD to AB and TV to RS)

4:  - From 1,2,3 AAS - If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the triangles are congruent (AAS)

5: CD = TV - CPCTC - Congruent Parts  Congruent Triangles Congruent

Friday, October 28, 2016

The measure of an exterior angle of a triangle equals the sum of the measures of the two nonadjacent interior angles

Exterior angle of a triangle
Exterior angle of a triangle
Given
Triangle ABC
  - Two adjacent angles form a straight line (BC)

Prove


Proof

2: - If the exterior sides of two adjacent angles form a straight line, these angles are supplementary

 - From 1 and 2