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.

Slides:



Advertisements
Similar presentations
8.6 Proportions & Similar Triangles
Advertisements

Proportions & Similar Triangles. Objectives/Assignments Use proportionality theorems to calculate segment lengths. To solve real-life problems, such as.
Properties of similar triangles. Warm Up Solve each proportion AB = 16QR = 10.5 x = 21y = 8.
Applying Properties 7-4 of Similar Triangles Warm Up
7.4-APPLYING PROPERTIES OF SIMILAR TRIANGLES
7-4 Applying Properties of similar triangles
Applying Properties 7-4 of Similar Triangles Warm Up
Using Proportional Relationships
Warm Up Solve each proportion AB = 16 QR = 10.5 x = 21.
7-4 Parallel Lines and Proportional Parts
Warm-Up What is the scale factor (or similarity ratio) of the following two triangles?
Using Proportional Relationships
Objectives Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems.
7.5 Proportions In Triangles
 Objectives:  Students will apply proportions with a triangle or parallel lines.  Why?, So you can use perspective drawings, as seen in EX 28  Mastery.
Holt McDougal Geometry 7-5 Using Proportional Relationships 7-5 Using Proportional Relationships Holt Geometry Warm Up Warm Up Lesson Presentation Lesson.
Geometry warm ups. 7-5 PROPORTIONS IN TRIANGLES Side-Splitter Theorem When two or more parallel lines intersect other lines, proportional segments are.
12.5 Proportions & Similar Triangles. Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then.
Warm Up Solve each proportion
Holt McDougal Geometry 3-4 Perpendicular Lines 3-4 Perpendicular Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz.
Holt Geometry 7-4 Applying Properties of Similar Triangles Warm Up Solve each proportion
8.6 Proportions & Similar Triangles
Using Proportional Relationships
7-3 Triangle Similarity: AA, SSS, SAS Warm Up Lesson Presentation
Using Proportional Relationships
DRILL Are these two triangles similar? (Explain).
Conditions for Parallelograms
3-4 Perpendicular Lines Warm Up Lesson Presentation Lesson Quiz
3-4 Perpendicular Lines Warm Up Lesson Presentation Lesson Quiz
8.6 Proportions & Similar Triangles
Objectives Students will learn to how to apply Triangle Proportionality theorem to find segment lengths.
8.6 Proportions & Similar Triangles
7-4 Applying Properties of Similar Triangles
Applying Properties 7-4 of Similar Triangles Warm Up
Objectives Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems.
Class Greeting.
Using Proportional Relationships
Applying Properties 7-4 of Similar Triangles Warm Up
3-4 Perpendicular Lines Warm Up Lesson Presentation Lesson Quiz
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.
Parallel Lines and Proportional Parts
Warm Up Solve each proportion
8.6 Proportions & Similar Triangles
LT 7.5 Apply Properties of Similar Triangles
3-4 Perpendicular Lines Warm Up Lesson Presentation Lesson Quiz
Using Proportional Relationships
3-4 Perpendicular Lines Warm Up Lesson Presentation Lesson Quiz
Objectives Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems.
Applying Properties 7-5 of Similar Triangles Warm Up
Applying Properties of Similar Triangles Warm Up Lesson Presentation
8.4 Properties of Similar Triangles
Objectives Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems.
Applying Properties of Similar Triangles Warm Up Lesson Presentation
LEARNING GOALS – LESSON 7:4
7.4 Applying Properties of Similar Polygons
Applying Properties 7-4 of Similar Triangles Warm Up
8.4 Proportionality Theorems and Applications
Applying Properties of Similar Triangles Warm Up Lesson Presentation
8.4 Proportionality Theorems and Applications
Warm Up Solve each proportion AB = 16 QR = 10.5 x = 21 y = 8.
Applying Properties 7-4 of Similar Triangles Warm Up
Warm Up Solve each proportion AB = 16 QR = 10.5 x = 21 y = 8.
8.6 Proportions & Similar Triangles
Applying Properties 7-4 of Similar Triangles Warm Up
Applying Properties 7-4 of Similar Triangles Warm Up
Warm Up Solve each proportion AB = 16 QR = 10.5 x = 21 y = 8.
3-4 Perpendicular Lines Warm Up Lesson Presentation Lesson Quiz
3-4 Perpendicular Lines Warm Up Lesson Presentation Lesson Quiz
Using Proportional Relationships
Presentation transcript:

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 Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry

7-4 Applying Properties of Similar Triangles Warm Up Solve each proportion AB = 16QR = 10.5 x = 21y = 8

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems. Objectives

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles (The pieces are proportional) (Top/Bottom=Top/Bottom)

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 1: Finding the Length of a Segment Find US. Substitute 14 for RU, 4 for VT, and 10 for RV. Cross Products Prop. US(10) = 56 Divide both sides by 10. It is given that, so by the Triangle Proportionality Theorem. COPY THIS SLIDE:

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Check It Out! Example 1 Find PN. Substitute in the given values. Cross Products Prop. 2PN = 15 PN = 7.5Divide both sides by 2. Use the Triangle Proportionality Theorem. COPY THIS SLIDE:

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles COPY THIS SLIDE: (If the pieces are proportional, then the line is parallel.)

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 2: Verifying Segments are Parallel Verify that. Since,. COPY THIS SLIDE:

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Check It Out! Example 2 AC = 36 cm, and BC = 27 cm. Verify that. Since,. COPY THIS SLIDE:

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles COPY THIS SLIDE: This is the same thing, but without a triangle: Top/Bottom=Top/Bottom

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 3: Art Application Suppose that an artist decided to make a larger sketch of the trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in., find LM and MN to the nearest tenth of an inch. COPY THIS SLIDE:

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 3 Continued Given 2-Trans. Proportionality Corollary Substitute 4.9 for KL, 4.5 for AB, and 2.6 for BC. Cross Products Prop.4.5(LM) = 4.9(2.6) Divide both sides by 4.5. LM  2.8 in.

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 3 Continued 2-Trans. Proportionality Corollary Substitute 4.9 for KL, 4.5 for AB, and 4.1 for CD. Cross Products Prop.4.5(MN) = 4.9(4.1) Divide both sides by 4.5. MN  4.5 in.

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Check It Out! Example 3 Use the diagram to find LM and MN to the nearest tenth.

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Given Check It Out! Example 3 Continued 2-Trans. Proportionality Corollary Substitute 2.6 for KL, 2.4 for AB, and 1.4 for BC. Cross Products Prop.2.4(LM) = 1.4(2.6) Divide both sides by 2.4. LM  1.5 cm

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Check It Out! Example 3 Continued 2-Trans. Proportionality Corollary Substitute 2.6 for KL, 2.4 for AB, and 2.2 for CD. Cross Products Prop.2.4(MN) = 2.2(2.6) Divide both sides by 2.4. MN  2.4 cm

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles The previous theorems and corollary lead to the following conclusion. COPY THIS SLIDE: (Left/Right=Left/Right)

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 4: Using the Triangle Angle Bisector Theorem Find PS and SR. Substitute the given values. Cross Products Property Distributive Property by the ∆  Bisector Theorem. 40(x – 2) = 32(x + 5) 40x – 80 = 32x COPY THIS SLIDE:

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 4 Continued Simplify. Divide both sides by 8. Substitute 30 for x. 40x – 80 = 32x x = 240 x = 30 PS = x – 2SR = x + 5 = 30 – 2 = 28= = 35

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Check It Out! Example 4 Find AC and DC. Substitute in given values. Cross Products Theorem So DC = 9 and AC = 16. Simplify. by the ∆  Bisector Theorem. 4y = 4.5y – 9 –0.5y = –9 Divide both sides by –0.5.y = 18

Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Classwork/Homework: 7.4 #’s:1-14all