BASIC PROPORTIONALITY THEOREM IF A LINE IS DRAWN II TO ONE SIDE OF A TRI. TO INTERSECT THE OTHER TWO SIDES IN DISTINCT POINTS, THEN THE OTHER TWO SIDES.

Slides:

Advertisements

Similar presentations

Concept: Use Similar Polygons

Advertisements

Test For Congruent Triangles. Test 1 3 cm 4 cm 3 cm Given three sides : SSS Two triangles are congruent if the three sides of one triangle are equal to.

Similarity in Triangles. Similar Definition: In mathematics, polygons are similar if their corresponding (matching) angles are congruent (equal in measure)

Honors Geometry Section 8.3 Similarity Postulates and Theorems.

5-7 Inequalities in Two Triangles

Objective: Determine if triangles in a coordinate plane are similar. What do we know about similar figures? (1)Angles are congruent (2)Sides are proportional.

4.1 Quadrilaterals Quadrilateral Parallelogram Trapezoid

3.4c: Identifying Similar Triangles p AA Similarity If 2 angles in 1 triangle are congruent to 2 angles in a 2 nd triangle, then the 2 triangles.

7-3 Proving Triangles Similar

Geometry Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.

Chapter 7.1 Common Core G.SRT.5 - Use…similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Objective –

Working with Ratio Segments PART 1 ~adapted from Walch Education.

By: Lazar Trifunovic and Jack Bloomfeld. A ratio is a number of a certain unit divided by a number of the same unit. A proportion is an equation that.

Mean Proportional.

8.6 Proportion and Similar Triangles

Chapter 7 Similarity. Definition: Ratio The angles of a pentagon are in ratio 4:2:5:5:2, find the measure of each angle 4x+2x+5x+5x+2x = x.

Triangle Similarity.

Agenda 1) Bell Work 2) Outcomes 3) Finish 8.4 and 8.5 Notes 4) 8.6 -Triangle proportionality theorems 5) Exit Quiz 6) Start IP.

3.4d: Geometric Mean p Arithmetic and Geometric Mean Arithmetic mean is to ADD the 2 numbers and divide by 2 ex. find the mean of 8 and

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Warm up 1.What is the ratio of the corresponding side lengths for two congruent triangles?

(AA, SSS, SAS). AA Similarity (Angle-Angle) If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar.

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

7.5 Proportions and Similar Triangles

8-3 Proving Triangles Similar M11.C B

Homework (day 36-Honors) p. 465 (11, 17, 19, 21, 23, 28, 31, 41) p. 474 (4, 8, 12, 18, 22, 30, 32, 40, 43, 46) Quiz next block (7.3, 7.4, 7.5)…TEST in.

Drill Write your homework in your planner Take out your homework Find all angle measures:

 By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C.

Section 7-4 Similar Triangles.

Chapter 7 Similarity.

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

 There are 3 ways to show two triangles are similar to each other. Those 3 ways are: 1. Angle-Angle Similarity Postulate. (AA~) 2. Side-Angle-Side Similarity.

Angle-Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Triangle Similarity Keystone Geometry. 2 Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding.

Geometry Section 6.6 Use Proportionality Theorems.

Warm Up Week 6. Section 8.6 Day 1 I will use proportionality theorems to calculate segment lengths. Triangle Proportionality If a line parallel.

6.6 – Use Proportionality Theorems. Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then.

Date: Topic: Proving Triangles Similar (7.6) Warm-up: Find the similarity ratio, x, and y. The triangles are similar. 6 7 The similarity ratio is: Find.

Section Review Triangle Similarity. Similar Triangles Triangles are similar if (1) their corresponding (matching) angles are congruent (equal)

7.1 Ratio and Proportions -Ratios: A comparison of 2 quantities -Proportion: A statement that 2 ratios are equal -Extended Proportion: When 3 or more ratios.

WARM UP 1) ABCD is a parallelogram. Find the measures of x and y.

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.

Triangle Properties and Congruent Triangles. Triangle Side Measures Try to make the following triangles with sides measuring: 5 cm, 8 cm, 16 cm 5 cm,

8.3 Methods of Proving Triangles Similar

Sect. 8.6 Proportions and Similar Triangles

Similarity Postulates

Applying Properties of Similar Triangles

INTRODUCTION Congruent figure:.

Section 11-7 Ratios of Areas.

Y. Davis Geometry Notes Chapter 7.

5.3 Proving Triangle Similar

Proving Triangles Similar

PARALLEL LINES AND PROPORTIONAL PARTS

7-4 Applying Properties of Similar Triangles

CHAPTER 7 SIMILAR POLYGONS.

5.3 Proving Triangle Similar

Proving Triangles Similar.

8.3 Methods of Proving Triangles Similar

Working with Ratio Segments (5.4.2)

Similar Triangles Panašūs trikampiai.

Proving Triangles Similar.

Triangle Midsegment Theorem – The segment joining the midpoints of any two sides will be parallel to the third side and half its length. If E and D are.

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

Ronald Hui Tak Sun Secondary School

Parallel Lines and Proportional Parts

Similar Triangles by Tristen Billerbeck

8.6 Proportion and Similar Triangles

Warm-Up Solve each proportion. 1) 2)

8.3 Methods of Proving Triangles are Similar Advanced Geometry 8.3 Methods of Proving    Triangles are Similar Learner Objective: I will use several.

Module 16: Lesson 4 AA Similarity of Triangles

Presentation transcript:

BASIC PROPORTIONALITY THEOREM IF A LINE IS DRAWN II TO ONE SIDE OF A TRI. TO INTERSECT THE OTHER TWO SIDES IN DISTINCT POINTS, THEN THE OTHER TWO SIDES ARE DIVIDED IN THE SAME RATIO.

CONVERSE OF BASIC PROPORTIONALITY THEOREM IF A LINE DIVIDES ANY TWO SIDES OF A TRI. IN THE SAME RATIO, THEN THE LINE IS II TO THE THIRD SIDE.

SIMILARITY CRITERIA AAA SIMILARITY CRITERION AA SIMILARITY CRITERION SSS SIMILARITY CRITERION SAS SIMILARITY CRITERION

AREA THEOREM THE RATIO OF THE AREAS OF TWO SIMILAR TRIANGLES ARE EQUAL TO THE RATIO OF THE SQUARES OF ANY TWO CRRESPONDING SIDES