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Benchmark 21 I can identify congruency theorems, SSS, SAS, ASA, AAS, and HL in diagrams
Side-Side-Side Postulate If three sides of a Δ are to three sides of another Δ, then the Δ’s are . A B C X YZ If AB XY, BC YZ, AC XZ, then ΔABC ΔXYZ
Side-Angle-Side Postulate If two sides and the included angle of a Δ are to two sides and the included angle of another Δ, then the Δ’s are . If AB XY, BC YZ, and
Angle-Side-Angle Postulate If 2 <‘s and the included side of a Δ are to 2 <‘s and the included side of another Δ, then the Δ’s are . A BC X YZ If
Angle-Angle-Side Theorem If 2 <‘s and a non-included side of a Δ are to 2 <‘s and a non-included side of another Δ, then the Δ’s are . If
Hypotenuse-Leg Theorem If hypotenuse and a leg of a Δ are to the hypotenuse and a leg of another Δ, then the Δ’s are . If AC XZ, and BC YZ then ΔABC ΔXYZ A B C X Y Z
What method is used to prove the triangles are congruent? SSSSAS AASASA
What method is used to prove the triangles are congruent? SASAAS SAS
What method is used to prove the triangles are congruent? SASAAS HLSAS
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Hypotenuse – Leg Congruence Theorem: HL. Hypotenuse-Leg Theorem (HL) If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and.
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8. BC = ED = 4; BC = EC = 3; DC = DC by Reflex so Δ BCD ΔEDC by SSS 9. KJ = LJ; GK = GL; GJ = GJ by Reflex so ΔGJK ΔGJL by SSS 12. YZ = 24, ST = 20,
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Benchmark 37 I can identify two triangles as similar using SSS, SAS, or AA triangle proportionality theorem.
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Triangle Proofs. USING SSS, SAS, AAS, HL, & ASA TO PROVE TRIANGLES ARE CONGRUENT STEPS YOU SHOULD FOLLOW IN PROOFS: 1. Using the information given, ______________.
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7/2/ : Analyzing Triangle Congruence Expectations: G2.3.1: Prove that triangles are congruent using the SSS, SAS, ASA, and AAS criteria and that.
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DO NOW!!! Solve for “x”.. Triangle Congruence SSS: Side Side Side If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles.
Similarity & Congruency Dr. Marinas Similarity Has same shape All corresponding pairs of angles are congruent Corresponding pairs of sides are in proportion.
4-4 & 4-5 Proving Triangles Congruent Objectives: 1. Use the SSS Postulate to test for triangle congruence. 2. Use the SAS Postulate to test for triangle.
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Do-Now 2) Find the value of x & the measure of each angle. 5x – 4 4x ° 1) Find the value of x. 4x x – 10 3x + 1 5x – 4 + 4x + 14 = 100 9x.
EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem Write a proof. SOLUTION Redraw the triangles so they are side by side with corresponding parts in the.
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