1 CHAPTER FOUR TRIANGLE CONGRUENCE Name Section 4...
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1 CHAPTER FOUR TRIANGLE CONGRUENCE 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
Transcript of 1 CHAPTER FOUR TRIANGLE CONGRUENCE Name Section 4...
1 CHAPTER FOUR TRIANGLE CONGRUENCE 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
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Classify each triangle by its side lengths. A. ABC
B. ABD C. ACD
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?
Find the side lengths of ∆ JKL.
3 Section 4-2: Angle Relationships in Triangles
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.
LT 3 I can apply the theorems about the interior and exterior angles of triangles to find angle measures.
4 Example 3: One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle? 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
5 Example 5: Applying the Exterior Angle Theorem Find m∠B. Example 6: Find m∠ACD.
Example 7: Find m∠K and m∠J.
6 Section 4-3: Congruent Triangles
LT 4 I can use properties of congruent triangles to find missing sides and angles.
LT 5 I can prove triangles are congruent by:
a. Definition of Congruence (4.3)
Define Corresponding Angles 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.
7 Example 3: Given: ∆ABC ≅ ∆DEF Find the value of x. 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
8 Section 4-4 Triangle Congruence: SSS and SAS
LT 5
I can prove triangles are congruent by:
b. SSS (4.4) c. SAS(4.4)
LT 6 I can apply theorems/postulates to solve problems about triangles using:
a. SSS (4.4) b. SAS(4.4)
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.
9 Example 4: Use SAS to explain why ∆ABC ≅ ∆DBC. 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
10 Lesson 4-5: Triangle Congruence: ASA, AAS, and HL
LT 5
I can prove triangles are congruent by: d. ASA(4.5) e. AAS(4.5) f. HL(4.5)
LT 6
I can apply theorems/postulates to solve problems about triangles using: d. ASA(4.5) e. AAS(4.5) f. HL(4.5)
Define Included side
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.
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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
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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.
13 Section 4-6: Triangle Congruence: CPCTC
LT 8 I will use CPCTC to prove parts of triangles are congruent.
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
14 Example 3: Given: PR bisects ∠QPS and ∠QRS. Prove: PQ ≅ PS Example 4: Given: NO || MP, ∠N ≅ ∠P Prove: MN || OP Example 5: Given: J is the midpoint of KM and NL. Prove: KL || MN
15 Section 4-8: Isosceles and Equilateral Triangles
LT 9 I can apply properties and theorems of isosceles and equilateral triangles to find missing side lengths and angle measures.
Define Isosceles Triangle Legs Vertex Angle Base Base angles Example 1: Find m∠F. Example 2: Find m∠G.
16 Example 3: Find m∠H. Example 4: Find m∠N.
Example 5: Find the value of x.
