CHAPTER FOUR TRIANGLE CONGRUENCE 1 Name Section 4-1: Classifying Triangles LT 1 I can classify triangles by their side lengths and their angles. LT 2 I will use triangle classification to find angle measures and side lengths. Triangles can be classified in two ways: by their side length or by their angle measure. Define: Equilateral triangle Isosceles triangle Scalene triangle Acute triangle Equiangular triangle Right triangle Obtuse triangle Classify each triangle by its angle measures. A FHG B. EFH C. EHG
2 Classify each triangle by its side lengths. A. ABC B. ABD C. ACD Find the side lengths of JKL. Find the side lengths of equilateral FGH. Music Application A manufacture produces musical triangles by bending pieces of steel into the shape of an equilateral triangle. The triangles are available in side of 4 inches, 7 inches, and 10 inches. How many 7-inch triangles can the manufacturer produce from a 100 inch piece of steel? How many 10-inch triangles can the manufacturer produce from a 100 inch piece of steel?
LT 3 Section 4-2: Angle Relationships in Triangles I can apply the theorems about the interior and exterior angles of triangles to find angle measures. 3 Define: Auxillary line Corollary Example 1: After an accident, the positions of cars are measured by law enforcement to investigate the collision. Use the diagram drawn from the information collected to find m XYZ and m YWZ. Example 2: Use the diagram to find m MJK.
Example 3: One of the acute angles in a right triangle measures 2x. What is the measure of the other acute angle? 4 Example 4: The measure of one of the acute angles in a right triangle is 48. What is the measure of the other acute angle? Define Interior Exterior Interior angle Exterior angle Remote interior angle
Example 5: Applying the Exterior Angle Theorem Find m B. 5 Example 6: Find m ACD. Example 7: Find m K and m J.
LT 4 LT 5 Section 4-3: Congruent Triangles I can use properties of congruent triangles to find missing sides and angles. I can prove triangles are congruent by: a. Definition of Congruence (4.3) Define Corresponding Angles 6 Corresponding Sides Congruent Polygons Example 1: Given: PQR STW Identify all pairs of corresponding congruent parts. Example 2: If polygon LMNP is congruent to polygon EFGH, identify all of the pairs of corresponding congruent parts.
Example 3: Given: ABC DEF Find the value of x. 7 Find m F. Example 4: Given: YWX and YWZ are right angles. YW bisects XYZ. W is the midpoint of XZ. XY YZ. Prove: XYW ZYW Example 5: Given: AD bisects BE. BE bisects AD. AB DE, A D Prove: ABC DEC
LT 5 LT 6 Section 4-4 Triangle Congruence: SSS and SAS I can prove triangles are congruent by: b. SSS (4.4) c. SAS(4.4) I can apply theorems/postulates to solve problems about triangles using: a. SSS (4.4) b. SAS(4.4) 8 Define: Triangle rigidity Included angle Example 1: Use SSS to explain why ABC DBC. Example 2: Use SSS to explain why ABC CDA. Example 3: The diagram shows part of the support structure for a tower. Use SAS to explain why XYZ VWZ.
Example 4: Use SAS to explain why ABC DBC. 9 Example 5: Show that the triangles are congruent for the given value of the variable. MNO PQR, when x = 5. Example 6: Given: BC AD, BC AD Prove: ABD CDB Example 7: Given: QP bisects RQS. QR QS Prove: RQP SQP
Lesson 4-5: Triangle Congruence: ASA, AAS, and HL I can prove triangles are congruent by: d. ASA(4.5) LT 5 e. AAS(4.5) f. HL(4.5) I can apply theorems/postulates to solve problems about triangles using: d. ASA(4.5) LT 6 e. AAS(4.5) f. HL(4.5) Define Included side 10 Example 1: Determine if you can use ASA to prove the triangles congruent. Explain. Example 2: Determine if you can use ASA to prove NKL LMN. Explain.
11 Example 3: Use AAS to prove the triangles congruent. Given: X V, YZW YWZ, XY VY Prove: XYZ VYW Example 4: Use AAS to prove the triangles congruent. Given: JL bisects KLM, K M Prove: JKL JML
12 Example 5: Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know. A) B) Example 6: Determine if you can use the HL Congruence Theorem to prove ABC DCB. If not, tell what else you need to know.
LT 8 Section 4-6: Triangle Congruence: CPCTC I will use CPCTC to prove parts of triangles are congruent. 13 Define CPCTC Example 1: A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond. What is JK? Example 2: Given: YW bisects XZ, XY YZ. Prove: XYW ZYW Z
Example 3: Given: PR bisects QPS and QRS. Prove: PQ PS 14 Example 4: Given: NO MP, N P Prove: MN OP Example 5: Given: J is the midpoint of KM and NL. Prove: KL MN
Section 4-8: Isosceles and Equilateral Triangles I can apply properties and theorems of isosceles and equilateral triangles to find missing side lengths and angle LT 9 measures. Define Isosceles Triangle Legs 15 Vertex Angle Base Base angles Example 1: Find m F. Example 2: Find m G.
Example 3: Find m H. 16 Example 4: Find m N. Example 5: Find the value of x.