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12/5: Identify congruent figures & their corresponding congruent parts Do Now On your desk: Agenda Homework Announcements Handout - Pencil & Calculator - Handouts from front Guided Practice Do Now: Write objective in notes Independent Practice Exit Ticket (15 problems) Test Corrections will replace Exam Retakes We will learn to… Identify congruent figures & their corresponding congruent parts Vocabulary size shape Congruent figures have the same _______ & _______ • Their corresponding parts (matching _______ sides and angles ) are _________________. congruent _________ Congruent Figures • Their corresponding parts are congruent, meaning: sides length o Matching _______have the same ________ angles measure o Matching _______have the same degree ________ Example 1: Naming Congruent Parts of Congruent Figures Angles: ∠E ≅ ∠S ∠D ≅ ∠R ∠F ≅ ∠T Sides: 𝑬𝑫 ≅ 𝑺𝑹 𝑬𝑭 ≅ 𝑺𝑻 𝑫𝑭 ≅ 𝑹𝑻 ∆EDF ≅ ∆SRT Triangle Congruence Statement: _________________ vertices in the same order Must list corresponding ___________ Example 2: Naming Congruent Parts of Congruent Figures from a Congruence Statement If HIJK≅LMNO, list the congruent corresponding parts. Angles: ∠H ≅ ∠L ∠I ≅ ∠M ∠J ≅ ∠N ∠K ≅ ∠O Sides: 𝑯𝑰 ≅ 𝑳𝑴 𝑰𝑱 ≅ 𝑴𝑵 𝑱𝑲 ≅ 𝑵𝑶 𝑯𝑲 ≅ 𝑳𝑶 Example 3: Using Congruent Figures to Solve for Missing Values LM = GH 8 = 2x – 3 11 = 2x x = 5.5 ∠N ≅ ∠E 72 = 7y + 9 63 = 7y 9=y Example 4: Check your understanding by completing alone! Given that ∆XYZ ≅ ∆RST, find the value of a. ∠Y ≅ ∠S 4a – 4 = 48 4a = 52 a = 13 Check Your Understanding! 1. Write a triangle congruence statement for the two triangles below: FGH ≅ Δ_______ JKH Δ_______ Check Your Understanding! 2. If you are given that ∆AUS ≅ ∆KAP, name the three pairs of congruent sides. 𝑨𝑼 ≅ 𝑲𝑨 𝑼𝑺 ≅ 𝑨𝑷 𝑨𝑺 ≅ 𝑲𝑷 Third Angles Theorem angles of one triangle are __________ congruent to two _______ If _____ two angles of ________ third another triangle, then the ______ angles are _________. congruent _______ Example 4: Using the Third Angles Theorem ∠M ≅ ∠T m∠M = m∠T 92⁰ = m∠T 180 – (52 + 36) 180 - 88 92⁰ Example 6: Applying the Third Angles Theorem Find the value of x. x = 15 Your Independent Practice Time • Prepare for ET – Complete HW due 12/7(A) and 12/8(B) • Can you answer these questions: – What is the Third Angles Theorem used for? showing two angles are congruent – How do you write a congruence statement? use vertices in correct order – What do we mean by congruent corresponding parts? sides and angles