1. Give the postulate or theorem that justifies why the triangles are similar. ANSWER AA Similarity Postulate 2. Solve = .

Slides:

Advertisements

Similar presentations

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.

Advertisements

Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles.

6.3Apply Properties of Chords Theorem 6.5 In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding.

Section 6 – 6 Use Proportionality Theorem. Theorems Triangle Proportionality Theorem – If a line parallel to one side of a triangle intersects the other.

Assignment P : 2-17, 21, 22, 25, 30, 31 Challenge Problems.

8.6 Proportions & Similar Triangles

Lesson 5-4: Proportional Parts

EXAMPLE 4 Find perimeters of similar figures Swimming

Proportions & Similar Triangles. Objectives/Assignments Use proportionality theorems to calculate segment lengths. To solve real-life problems, such as.

Warm-Up Exercises 1. What measure is needed to find the circumference or area of a circle? 2. Find the radius of a circle with diameter 8 centimeters.

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

Chapter 7: Proportions and Similarity

Finding Lengths of Segments in Chords When two chords intersect in the interior of a circle, each chord is divided into two segments which are called segments.

7-4 Parallel Line and Proportional Parts. You used proportions to solve problems between similar triangles. Use proportional parts within triangles. Use.

Find the length of a segment

7.5 Proportions & Similar Triangles

Chapter 7 Quiz Review Lessons

5.3 Theorems Involving Parallel Lines

7-4 Parallel Lines and Proportional Parts

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

Objective: Students will use proportional parts of triangles and divide a segment into parts. S. Calahan 2008.

Chapter 6.6 Notes: Use Proportionality Theorems Goal: You will use proportions with a triangle or parallel lines.

Bell Ringer. Proportions and Similar Triangles Example 1 Find Segment Lengths Find the value of x. 4 8 x 12 = Substitute 4 for CD, 8 for DB, x for CE,

4.8 Use Isosceles and Equilateral Triangles

7.5 Proportions In Triangles

Section 7-4 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 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.

 Objectives:  Students will apply proportions with a triangle or parallel lines.  Why?, So you can use perspective drawings, as seen in EX 28  Mastery.

The product of the means equals the product of the extremes.

10.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply Properties of Chords.

Warm-Up 1 In the diagram, DE is parallel to AC. Name a pair of similar triangles and explain why they are similar.

6.6 Use Proportionality Theorems. Objectives  Use proportional parts of triangles  Divide a segment into parts.

Similarity Chapter Ratio and Proportion  A Ratio is a comparison of two numbers. o Written in 3 ways oA to B oA / B oA : B  A Proportion is an.

12.5 Proportions & Similar Triangles. Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then.

Proportions and Similar Triangles Section 7.5. Objectives Use the Triangle Proportionality Theorem and its converse.

1. DC Tell whether the segment is best described as a radius,

8.6 Proportions & Similar Triangles

Triangle Proportionality

Use Properties of Tangents

4.3 Warm Up Are the triangles similar? If so, which theorem justifies your answer.

Applying Properties of Similar Triangles

1. Give the postulate or theorem that justifies why the triangles are similar. ANSWER AA Similarity Postulate 2. Solve = .

Proportional Lengths Unit 6: Section 7.6.

DRILL Are these two triangles similar? (Explain).

7.5 ESSENTIAL QUESTION: How do you use the Triangle Proportionality Theorem and its Converse in solving missing parts?

Chapter 7 Proportions & Similarity

8.6 Proportions & Similar Triangles

Objectives Students will learn to how to apply Triangle Proportionality theorem to find segment lengths.

Chapter 6.6 Notes: Use Proportionality Theorems

Theorems Involving Parallel Lines and Triangles

Lesson 7-6 Proportional Lengths (page 254)

Proportionality Theorems

8.6 Proportions & 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.

CHAPTER 7 SIMILAR POLYGONS.

Proportionality Theorems

8.6 Proportions & Similar Triangles

EXAMPLE 1 Use congruent chords to find an arc measure

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles 7-4 Applying Properties of Similar Triangles Holt Geometry Warm Up Warm Up Lesson Presentation.

EXAMPLE 1 Identify special segments and lines

Geometry 8.4 Proportionality Theorems

8.6 Proportions & Similar Triangles

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.

Apply Properties of Chords

8.6 Proportions & Similar Triangles

Presentation transcript:

1. Give the postulate or theorem that justifies why the triangles are similar. ANSWER AA Similarity Postulate 2. Solve = . 16 32 12 – x x ANSWER 8

Find the length of a segment 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 RQ QU RS ST = Triangle Proportionality Theorem RQ 9 4 6 = Substitute. RQ = 6 Multiply each side by 9 and simplify.

EXAMPLE 2 Solve a real-world problem On the shoerack shown, AB = 33 cm, BC = 27 cm, CD = 44 cm,and DE = 25 cm, Explain why the gray shelf is not parallel to the floor. Shoerack SOLUTION Find and simplify the ratios of lengths determined by the shoerack. CD DE 44 25 = CB BA 27 33 = 9 11

EXAMPLE 2 Solve a real-world problem Because , BD is not parallel to AE . So, the shelf is not parallel to the floor. 44 25 9 11 = ANSWER

GUIDED PRACTICE for Examples 1 and 2 1. Find the length of YZ . 315 11 ANSWER 2. Determine whether PS || QR . ANSWER parallel

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 Main Street and South Main Street. City Travel SOLUTION Corresponding angles are congruent, so FE, GD , and HC are parallel. Use Theorem 6.6.

The distance between Main Street and South Main Street is 360 yards. EXAMPLE 3 Use Theorem 6.6 HG GF CD DE = Parallel lines divide transversals proportionally. HG + GF GF CD + DE DE = Property of proportions (Property 4) HF 120 300+150 150 = Substitute. 450 150 HF 120 = Simplify. HF = 360 Multiply each side by 120 and simplify. The distance between Main Street and South Main Street is 360 yards.

EXAMPLE 4 Use Theorem 6.7 In the diagram, QPR RPS. Use the given side lengths to find the length of RS . ~ SOLUTION Because PR is an angle bisector of QPS, you can apply Theorem 6.7. Let RS = x. Then RQ = 15 – x.

EXAMPLE 4 Use Theorem 6.7 RQ RS PQ PS = 15 – x x = 7 3 7x = 195 – 13x Angle bisector divides opposite side proportionally. 15 – x x = 7 3 Substitute. 7x = 195 – 13x Cross Products Property x = 9.75 Solve for x.

GUIDED PRACTICE for Examples 3 and 4 Find the length of AB. 3. ANSWER 19.2 4. ANSWER 2 4

Daily Homework Quiz Find the value of the variable. 1. ANSWER 12

Daily Homework Quiz Find the value of the variable. 2. ANSWER 13.5

Daily Homework Quiz Find the value of the variable. 3. ANSWER 23.8

Daily Homework Quiz 4. This diagram represents a tract of land being developed for homes. Which lot has the greatest perimeter? ANSWER Lot C