Geometry- Triangle Proofs

SAS (side, angle, side)

If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Vertical Angles

*Information comes from the diagram (no givens). Statements: 1. ∠A≅∠B Reasons: 1. Vertical ∠s are ≅

Reflexive Property

*Information comes from the diagram (no givens). Statements: 1. RN≅RN Reasons: 1. Reflexive Property

Perpendicular Lines

*Makes right angles Given: AD⊥BC Prove: ∠BDA≅∠CDA Statements: Reasons: 1. AD⊥BC 2. ∠ADB and ∠ADC are right angles 3. ∠BDA≅∠CDA Reasons: 1. Given 2. Perpendicular lines form right angles 3. All right angles are ≅

Bisector

*Must write the given Given: AD bisects BC Prove: BD≅CD Statements: 1. AD bisects BC 2. BD≅CD Reasons: 1. Given 2. Definition of bisector

Midpoint

*Must write the given Given: D is the midpoint of BC Prove: BD≅CD Statements: 1. D is the midpoint of BC 2. BD≅CD Reasons: 1. Given 2. Definition of midpoint

What can you NOT use to prove that two triangles are congruent?

1. SSA 2. AAA 3. ASS

What are the five possible ways to prove that two triangles are congruent?

1. SSS 2. ASA 3. SAS 4. AAS 5. HL

Angle Bisector

Given: AD bisects ∠BAC Prove: ∠BAD≅∠CAD Statements: 1. AD bisects ∠BAC 2. ∠BAD≅∠CAD Reasons: 1. Given 2. Definition of angle bisector

SSS (side, side, side)

If 3 sides of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

HL (hypotenuse, leg)

If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

AAS (angle, angle, side)

If two angles and a side opposite one of the angles in one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

ASA (angle, side, angle)

If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Isosceles Triangle

Statements: 1. 🔼ABC is an isosceles triangle 2. ∠ABC≅∠ACB Reasons: 1. Given 2.