Math & Geometry
Sunday, November 13, 2016
Wednesday, November 9, 2016
If two sides of a triangle are congruent, then the angles opposite these sides are also congruent
Given
Isosceles triangle ABC, AB = AC
Prove
Proof
1: AB = AC - Given
2: Draw angle bisector AO from A to BC
3: - The bisector of the vertex angle of an isosceles triangle separates the triangle into two congruent triangles
4: - CPCTC (Corresponding parts of congruent triangles are congruent)
Isosceles triangle ABC, AB = AC
Prove
Proof
1: AB = AC - Given
2: Draw angle bisector AO from A to BC
3: - The bisector of the vertex angle of an isosceles triangle separates the triangle into two congruent triangles
4: - CPCTC (Corresponding parts of congruent triangles are congruent)
Tuesday, November 8, 2016
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 |
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
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).
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).
Saturday, November 5, 2016
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
Given
Triangles ABC, EFG
Prove
Proof
1:
- Given
2: - From 1
3:
- In a triangle, the sum of the measures of the interior angles is 180°
4: - From 3
5: - substitute 2 in 4
6: - From 5
Triangles ABC, EFG
Prove
Proof
1:
- Given
2: - From 1
3:
- In a triangle, the sum of the measures of the interior angles is 180°
4: - From 3
5: - substitute 2 in 4
6: - From 5
Friday, November 4, 2016
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
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