Notes Lesson 5.2 Congruent Triangles Target 4.1

What information is sufficient to prove triangles congruent? Congruent Figures Lesson 5.2 Definition: Congruent triangles are triangles that have all corresponding sides congruent and all corresponding angles congruent. Write a congruence statement for the triangles at the left. What information is sufficient to prove triangles congruent?

Find the value of x and the lengths of the given sides. Congruent Figures Target 4.1 Example 2: XYZ KLM, YZ= x + 10 LM= 2x Find the value of x and the lengths of the given sides. Begin marking these triangles with corresponding angles that are congruent.

Leading to Target 4.2

Triangle Congruence by SSS and SAS Lesson 5.3

Write a two-column proof. Triangle Congruence by ASA and AAS Example 3: Write a two-column proof. Given: A B, AP BP Prove: APX BPY 1 2 1 2 Statements Reasons 1. 1. Given 2. 2. Vertical angles are congruent. 3. 3. ASA

Write a two-column proof that uses AAS. Given: B D, AB || CD Triangle Congruence by ASA and AAS Example 4: TARGET 4.3 & 4.5 Given 2 Not an included side 1 Write a two-column proof that uses AAS. Given: B D, AB || CD Prove: ABC CDA Statements Reasons 1. B D, AB || CD 1. Given 2. 1 2 2. If lines are ||, then alternate interior angles are . 3. AC CA 3. Reflexive Property of Congruence 4. ABC CDA 4. AAS Theorem

Triangle Congruence by SSS and SAS Target 4.2 Example 5: Copy the diagram. Mark the congruent sides. Given: M is the midpoint of XY, AX AY Prove: AMX AMY From the given information, can you prove that the triangles are congruent. Explain. Midpoint M implies MX MY. AM AM by the Reflexive Property of Congruence. AMX AMY by the SSS Postulate.

a) Draw the two congruent triangles separately. Triangle Congruence by SSS and SAS Target 4.2 Example 6: A B a) Draw the two congruent triangles separately. a) D C C D b) DC CD by the Reflexive Property. You now have two pairs of corresponding congruent sides. Therefore if you know ADC BCD, you can prove ADC BCD by SAS. b) AD BC. What other information do you need to prove ADC BCD by SAS? Edit text. See page 62. GEOM_3eTP04_58-74_MQ

TARGET 4.3 YOU TRY #1 A

Review: Right triangle: Hypotenuse Leg H L L Leg TARGET 4.4

What additional information is needed to prove. Prove: ABC DCB by HL. Congruence in Right Triangles TARGET 4.4 Example 7: What additional information is needed to prove. Prove: ABC DCB by HL. C C D B A B Since BC CB Reflexive Property of Congruence You must prove that BD CA To prove ABC DCB by the (HL Theorem).

Congruence in Right Triangles TARGET 4.4 Example 8: One student wrote “ CPA MPA by SAS” for the diagram below. Is the student correct? Explain. The diagram shows the following congruent parts. CA MA CPA MPA PA PA The congruent angles are not included between the corresponding congruent sides. The triangles are not congruent by the SAS Postulate, but they are congruent by the HL Theorem.

YOU TRY #2 TARGET 4.4 What additional information will allow you to prove the triangles congruent by the HL theorem? C

YOU TRY #3 TARGET 4.4 C