6.3 Similar Triangles.

Slides:

Advertisements

Similar presentations

Similar Triangles. What does similar mean? Similar—the same shapes, but different sizes (may need to be flipped or turned) 4 ft 8ft 12 ft 3ft 6 ft.

Advertisements

Shortcuts to Triangle Similarity Example 3-1a In the figure, and Determine which triangles in the figure are similar Vertical angles are congruent,

7-3: Identifying Similar Triangles

7-3 Proving Triangles Similar

Lesson 6-3 Similar Triangles. Ohio Content Standards:

Benchmark 37 I can identify two triangles as similar using SSS, SAS, or AA triangle proportionality theorem.

5-Minute Check on Lesson 6-2

Chapter 7: Proportions and Similarity

Lesson: 9 – 3 Similar Triangles

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 7–2) NGSSS Then/Now Postulate 7.1: Angle-Angle (AA) Similarity Example 1: Use the AA Similarity.

Side Splitting Theorem 8.4. Identify parallel lines in triangles. homework Learn the side splitting theorem. Use the side splitting theorem to solve problems.

Geometry 7-2 Solving Similar Δ’s Proportions can be used to find the missing lengths of similar figures. Ex) ΔCAB ~ ΔTRS. Find RT.

Similar Triangles Similar Triangles – Two triangles are similar if and only if there is a correspondence between their vertices such that their corresponding.

Concept. Example 1 Use the AA Similarity Postulate A. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.

Lesson 3 Menu 1.The quadrilaterals are similar. Write a similarity statement and find the scale factor of the larger quadrilateral to the smaller quadrilateral.

Section 7.3 Similar Triangles.

Warm-Up Since they are polygons, what two things must be true about triangles if they are similar?

Geometry Sections 6.4 and 6.5 Prove Triangles Similar by AA Prove Triangles Similar by SSS and SAS.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 7–2) CCSS Then/Now Postulate 7.1: Angle-Angle (AA) Similarity Example 1: Use the AA Similarity.

6.3 Similar Triangles.

 Then: You used AAS, SSS, and SAS Congruence Theorems to prove triangles congruent.  Now: 1. Identify similar triangles using the AA Similarity Postulate.

Lesson 8.4. If we know that two triangles are congruent, we can use the definition of congruent triangles (CPCTC) to prove that pairs of angles and sides.

Honors Geometry Section 8.6 Triangle Proportionality Theorem.

Geometry Review for Test Know your proportions Label Answers Show Work.

Triangle Similarity Advanced Geometry Similarity Lesson 3.

Chapter 7 Lesson 4: Parallel Lines and Proportional Parts Geometry CP Mrs. Mongold.

Showing Triangles are Similar: AA, SSS and SAS

Indirect Measurement. Indirect Measurement: Allows you to use properties of similar polygons to find distances or lengths that are difficult to measure.

LESSON 7–3 Similar Triangles.

7.4 Showing Triangles are Similar: SSS and SAS

Sections 6.3 & 6.4 Proving triangles are similar using AA, SSS, SAS

Warm up… checkpoint quiz page 429 #’s 1 – 10.

Similarity Postulates

Take a warm-up from the ChromeBook, calculator, and compass

Identify similar triangles Use similar triangles to solve problems

Similar Triangles.

7.3 Similar Triangles.

Check HW/Work on warm-up

Similar Triangles Chapter 7-3.

Chapter 7: Proportions and Similarity Proportions Make a Frayer foldable 7.1 Ratio and Proportion.

7-3: Proving Triangles are Similar

Determine whether the triangles are similar.

Similar Figures Chapter 5.

D. N. A. 1) Are the following triangles similar? PQRS~CDAB

7.3 Proving Triangles Similar

7.5 Parts of Similar Triangles

Proving Triangles Similar Related Topic

Similar Triangles Chapter 7-3 TARGETS Identify similar triangles.

Warm Up #24 1. If ∆QRS  ∆ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion Q  Z; R.

Congruencies and Proportions in Similar Triangles

∆JKL ∼ ∆MNO with a scale factor of 5:6

Proving Triangles Similar.

Similar Figures.

7.3: Similar Triangles Similar triangles have congruent corresponding angles and proportional corresponding sides Z Y A C X B angle A angle X angle.

6.5 Parts of Similar Triangles

Agenda Investigation 8-3 Proving Triangles are Similar Class Work

Similar Figures To find an unknown side length in similar figures:

6.3 AA Similarity Geometry.

Proving Triangles Similar.

Week 5 Warm Up Add theorem 2.1 here next year.

Similar Similar means that the corresponding sides are in proportion and the corresponding angles are congruent. (same shape, different size)

Agenda Investigation 8-3 Proving Triangles are Similar Class Work

7.3 Similar Triangles (~s)

Module 16: Lesson 4 AA Similarity of Triangles

Presentation transcript:

6.3 Similar Triangles

Similar Triangles AA Similarity 2 s of a Δ are  to 2 s of another Δ SSS Similarity corresponding sides of 2 Δs are proportional SAS Similarity corresponding sides of 2 Δs are proportional and the included s are 

Example 1: In the figure, AB is parallel to DC, BE = 27, DE = 45, AE = 21 and CE =35. Determine which triangles in the figure are similar.

Your Turn: In the figure, OW = 7, BW = 9, WT = 17.5, and WI = 22.5. Determine which triangles in the figure are similar.

Your Turn: Find AC and CE.

Example 3: INDIRECT MEASUREMENT Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 P.M. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time. What is the height of the Sears Tower?

Assignment Geometry Pg. 302 # 10 – 20, WB 6-3 Honors Geometry Pg. 302 #10 – 28, WB 6-3