EXAMPLE 5 Use a scale factor In the diagram, ∆ TPR ~ ∆ XPZ. Find the length of the altitude PS. SOLUTION First, find the scale factor of ∆ TPR to ∆ XPZ.

Slides:

Advertisements

Similar presentations

EXAMPLE 2 Find the scale factor

Advertisements

EXAMPLE 2 Find a leg length ALGEBRA Find the value of x. SOLUTION Use the tangent of an acute angle to find a leg length. tan 32 o = opp. adj. Write ratio.

EXAMPLE 1 Find the length of a segment In the diagram, QS || UT, RS = 4, ST = 6, and QU = 9. What is the length of RQ ? SOLUTION Triangle Proportionality.

EXAMPLE 2 Find the scale factor Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor of ZYXW.

Use the cross products property EXAMPLE 1 Write original proportion = x 6 Solve the proportion =. 8 x 6 15 Cross products property Simplify. 120.

Find hypotenuse length in a triangle EXAMPLE 1

EXAMPLE 2 Using the Cross Products Property = 40.8 m Write original proportion. Cross products property Multiply. 6.8m 6.8 = Divide.

EXAMPLE 4 Find perimeters of similar figures Swimming A town is building a new swimming pool. An Olympic pool is rectangular with length 50 meters and.

Write decimal as percent. Divide each side by 136. Substitute 51 for a and 136 for b. Write percent equation. Find a percent using the percent equation.

Lesson 6-5 Parts of Similar Triangles. Ohio Content Standards:

EXAMPLE 5 Find leg lengths using an angle of elevation SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14 feet and an angle of elevation.

EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.

EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.

EXAMPLE 4 Find perimeters of similar figures Swimming

EXAMPLE 1 Identify similar triangles Identify the similar triangles in the diagram. SOLUTION Sketch the three similar right triangles so that the corresponding.

EXAMPLE 2 Find a leg length ALGEBRA Find the value of x. SOLUTION Use the tangent of an acute angle to find a leg length. tan 32 o = opp. adj. Write ratio.

Ex. 3: Why a Line Has Only One Slope

Over Lesson 7–3 Determine whether the triangles are similar. Justify your answer. Determine whether the triangles are similar. Justify your answer. Determine.

8.1 Similar Polygons. What is a ratio? An expression that compares two quantities by division Can be written in 3 ways.

Indirect Measurement and Additional Similarity Theorems 8.5.

8.4 Similar Triangles Geometry Mr. Parrish. Objectives/Assignment Identify similar triangles. Use similar triangles in real-life problems such as using.

EXAMPLE 1 Identify similar solids Tell whether the given right rectangular prism is similar to the right rectangular prism shown at the right. a. b.

Similar Right Triangles

Bell Ringer Similar Polygons Two polygons are similar polygons if corresponding angles are congruent and corresponding side length are proportional.

EXAMPLE 4 Find a hypotenuse using an angle of depression SKIING

1 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt Ratios/ Proportions Similar.

Find the length of a segment

6.3 – Use Similar Polygons Two polygons are similar polygons if corresponding angles are congruent and corresponding side lengths are proportional. In.

Chapter 6.3 Notes: Use Similar Polygons

Geometry 6.3 Big Idea: Use Similar Polygons

Unit 6 Part 1 Using Proportions, Similar Polygons, and Ratios.

Warm-Up What is the scale factor (or similarity ratio) of the following two triangles?

Similar Figures and Scale Drawings

EXAMPLE 1 Identify similar triangles

EXAMPLE 3 Use Theorem 6.6 In the diagram, 1, 2, and 3 are all congruent and GF = 120 yards, DE = 150 yards, and CD = 300 yards. Find the distance HF between.

EXAMPLE 1 Use similarity statements b. Check that the ratios of corresponding side lengths are equal. In the diagram, ∆RST ~ ∆XYZ a. List all pairs of.

EXAMPLE 2 Find cosine ratios Find cos U and cos W. Write each answer as a fraction and as a decimal. cos U = adj. to U hyp = UV UW = cos W.

EXAMPLE 1 Draw a dilation with a scale factor greater than 1

EXAMPLE 1 Use similarity statements b. Check that the ratios of corresponding side lengths are equal. In the diagram, ∆RST ~ ∆XYZ a. List all pairs of.

Use Similar Polygons Warm Up Lesson Presentation Lesson Quiz.

SIMILARITY April 25, Brief Review Medians  What is a median?

Similar Polygons NOTES 8.1 Goals 1)Use Similarity Statements 2)Find corresponding lengths in similar polygons 3)Find perimeters & areas of similar polygons.

Groundhog Day A 16 inch tall groundhog emerges on Groundhog Day near a tree and sees its shadow. The length of the groundhog’s shadow is 5 inches, and.

6.3a Using Similar Polygons Objective: Use proportions to identify similar polygons.

EXAMPLE 3 Find the area of an isosceles triangle

ESSENTIAL QUESTION: How do you calculate the area of triangles?

Use proportions to identify similar polygons.

7.5 Parts of Similar Triangles

The Converse of the Pythagorean Theorem

EXAMPLE 2 Find cosine ratios

Solve an equation by multiplying by a reciprocal

Using Proportions To Solve For Missing Sides

Objective: Use proportions to identify similar polygons

7-5 Parts of Similar Triangles

Chapter 6.3 Notes: Use Similar Polygons

Similar Polygons.

Use proportions to identify similar polygons.

Test study Guide/Breakdown

8.4 Similar Triangles.

Class Greeting.

Parts of Similar Triangles

Find the values of the variables.

6-1: Use Similar Polygons

Corresponding Parts of Similar Triangles

Standardized Test Practice

EXAMPLE 1 Use similarity statements In the diagram, ∆RST ~ ∆XYZ

1. Solve = 60 x ANSWER The scale of a map is 1 cm : 10 mi. The actual distance between two towns is 4.3 miles. Find the length on the.

Find the values of the variables.

Similar Triangles.

Presentation transcript:

EXAMPLE 5 Use a scale factor In the diagram, ∆ TPR ~ ∆ XPZ. Find the length of the altitude PS. SOLUTION First, find the scale factor of ∆ TPR to ∆ XPZ. TR XZ = = = 3 4

EXAMPLE 5 Use a scale factor Because the ratio of the lengths of the altitudes in similar triangles is equal to the scale factor, you can write the following proportion. The length of the altitude PS is 15. Write proportion. Substitute 20 for PY. Multiply each side by 20 and simplify. PS PY 3 4 = PS = = PS 15 ANSWER

GUIDED PRACTICE for Example 5 In the diagram, ABCDE ~ FGHJK. In the diagram, ∆JKL ~ ∆ EFG. Find the length of the median KM. 7.

GUIDED PRACTICE for Example 5 JL EG First find the scale factor of ∆ JKL to ∆ EFG. SOLUTION = = = 6 5 Because the ratio of the lengths of the median in similar triangles is equal to the scale factor, you can write the following proportion.

GUIDED PRACTICE for Example 5 SOLUTION KM = 42 KM HF = 6 5 KM 35 = 6 5 Write proportion. Substitute 35 for HF. Multiply each side by 35 and simplify.