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Geometry Today: HW Check 7.3 Instruction Practice I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end.

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Presentation on theme: "Geometry Today: HW Check 7.3 Instruction Practice I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end."— Presentation transcript:

1 Geometry Today: HW Check 7.3 Instruction Practice I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end. Larry Bird

2 Yesterday Assignment: 7.2 p 473#13, 15, 19, 29, 35, 37, 51, 57 Quiz 7.1-7.3 on Friday I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end. Larry Bird

3 Example 1 A.Yes; ΔABC ~ ΔFGH B.Yes; ΔABC ~ ΔGFH C.Yes; ΔABC ~ ΔHFG D.No; the triangles are not similar. 1. Determine whether the triangles are similar. If so, write a similarity statement. 4 8 12 6 2 3

4 Example 3 A.1.2 B.2.1 C.7.2 D.9.3 2. The two polygons are similar. Solve for b.

5 Example 1 A.Yes; ΔWVZ ~ ΔYVX B.Yes; ΔWVZ ~ ΔXVY C.Yes; ΔWVZ ~ ΔXYV D.No; the triangles are not similar. 3. Determine whether the triangles are similar. If so, write a similarity statement.

6 7.3 Similar Triangles Objectives: 1.Identify similar triangles 2.Use similar triangles in real life Vocabulary: AA ~, SSS~, SAS~

7 CCSS Content Standards G.SRT.4 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 4 Model with mathematics. 7 Look for and make use of structure.

8 Then/Now You used the AAS, SSS, and SAS Congruence Theorems to prove triangles congruent. Identify similar triangles using the AA Similarity Postulate and the SSS and SAS Similarity Theorems. Use similar triangles to solve problems.

9 Angle-Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. J K L X Z Y If  K   Y and  J   X, then  JKL   XYZ.

10 Example 1 A.Yes; ΔABC ~ ΔFGH B.Yes; ΔABC ~ ΔGFH C.Yes; ΔABC ~ ΔHFG D.No; the triangles are not similar. 1. Determine whether the triangles are similar. If so, write a similarity statement. 4 8 12 6 2 3

11 Side-Side-Side (SSS) Similarity Theorem If the corresponding sides of two triangles are proportional, then the triangles are similar. If, then  ABC ~  PQR A B C Q P R

12 If AC = 6, AD = 10, BC = 9, CE = 6, AB = 6 and ED = 4 is  ACB ~  DCE? D A B C E What is the scale factor?

13 Side-Angle-Side (SAS) Similarity Theorem If an angle of one triangle is congruent to an angle of a second triangle, and the lengths of the sides including these angles are proportional, then the triangles are similar. Y X Z M P N

14 Are these triangles similar? If yes, what is the scale factor? If yes, what is the similarity statement? Given:  XYZ: XY = 5, YZ = 4, m  Z = 50°  UVW: UV = 10, VW = 8, m  W = 50°

15 Are the triangles below similar? W X Y Z V Are these triangles similar? If yes, what is the scale factor? If yes, what is the similarity statement? 4 2

16 A museum worker is attempting to check the dinosaur’s eyes. Unfortunately, the snout is too wide and he can not get a clear view. To get a better look, he places a mirror on the ground and uses the reflections. If the worker’s eyes are 5.5’ high and the mirror is 12’’ from the man and 2’ from the dinosaur, what is the height of the dinosaur?

17 To find the distance across a lake you form two isosceles triangles. What is the length of the lake? 90’ 180’ 120’

18 Assignment: 7.3 p 483 #5, 9, 11, 13, 19, 21, 23, 29 Geometry I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end. Larry Bird


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