GBK Geometry
Today's lesson focuses on the Angle-Angle (AA) Similarity Theorem, including test analysis and proving triangle similarity through given angles. We will explore triangles ΔABC and ΔDEF, proving that if ∠A = ∠D and ∠B = ∠E, then ΔABC is similar to ΔDEF (ΔABC ~ ΔDEF). Additionally, we'll cover transitivity of similarity through another proof. Homework includes problem assignments #68, #69, or #70. Remember to clean up the classroom before leaving. See you tomorrow!
GBK Geometry
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Presentation Transcript
GBK Geometry Jordan Johnson
Today’s plan • Greeting • Hand in Unit 9 Test Analysis • AA Similarity Proof • Homework / Questions • Clean-up
The AA Similarity Theorem • Given: • ΔABC and ΔDEF • A = D and B = E • Prove:ΔABC ~ ΔDEF • Setup: • ΔABC is either larger, smaller, or congruent to ΔDEF • If ΔABC ΔDEF, ΔABC ~ ΔDEF by our previous proof. • Suppose (without loss of generality) ΔABC is larger. • AB > DE, so choose point X on AB such that AX = DE, and choose point Y on AC such that AXY = E.
Homework • 25+ minutes: • Asg #68, #69, or #70. • Prove using the AA Theorem: • Theorem: Similarity (of triangles) is transitive. • Given:ABC ~ XYZ and XYZ ~ DEF. • Prove:ABC ~ DEF.
Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!
