Prove Triangles Congruent by SAS

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Presentation transcript:

Prove Triangles Congruent by SAS 4.9 Prove Triangles Congruent by SAS Side-Angle-Side (SAS) Congruence Postulate 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 two triangles are congruent. S R T V U W

Prove Triangles Congruent by SAS 4.9 Prove Triangles Congruent by SAS Example 1 Use the SAS Congruence Postulate M N L R S T Solution It is given that and __________. SAS Congruence Postulate So, by the ____________________________,

Prove Triangles Congruent by SAS 4.9 Prove Triangles Congruent by SAS Hypotenuse-Leg Congruence Theorem If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are ___________. B A C E D F congruent

Prove Triangles Congruent by SAS 4.9 Prove Triangles Congruent by SAS Example 2 Use the HL Congruence Theorem B A C D E Write a proof. Given: Prove: Statements Reasons Given Given

Prove Triangles Congruent by SAS 4.9 Prove Triangles Congruent by SAS Example 2 Use the HL Congruence Theorem B A C D E Write a proof. Given: Prove: Statements Reasons right angles right right triangles triangle

Prove Triangles Congruent by SAS 4.9 Prove Triangles Congruent by SAS Example 2 Use the HL Congruence Theorem B A C D E Write a proof. Given: Prove: Statements Reasons Given HL Congruence Theorem

Prove Triangles Congruent by SAS 4.9 Prove Triangles Congruent by SAS Checkpoint. Complete the following exercises. Decide whether enough information is given to prove ABC LMN using the SAS Congruence Postulate. A B C Sides: N M L Included angle: Therefore there is enough information

Prove Triangles Congruent by SAS 4.9 Prove Triangles Congruent by SAS Checkpoint. Complete the following exercises. P S Q R Write a proof. Given: Prove: Statements Reasons Given Given Definition of perp. lines Definition of a right triangle

Prove Triangles Congruent by SAS 4.9 Prove Triangles Congruent by SAS Checkpoint. Complete the following exercises. P S Q R Write a proof. Given: Prove: Statements Reasons Reflexive Property of Cong. HL Congruence Theorem

Prove Triangles Congruent by SAS 4.9 Prove Triangles Congruent by SAS Pg. 262, 4.9 #1-16