Use Similar Polygons & AA Postulate

Slides:

Advertisements

Similar presentations

Concept: Use Similar Polygons

Advertisements

7.4 A Postulate for Similar Triangles. We can prove that 2 triangles are similar by showing that all 3 corresponding angles are congruent, and all 3 sides.

Congruence and Similarity

7-3 Proving Triangles Similar

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

Using Proportions to Solve Geometry Problems Section 6.3.

Ratio of Similitude. The ratio of similitude of two similar polygons is the ratio of the lengths of any two corresponding sides. C’ B’ A’ C B A It doesn’t.

 When two objects are congruent, they have the same shape and size.  Two objects are similar if they have the same shape, but different sizes.  Their.

Solve the following proportions. a = 9 b = 7 c = 6 d = 6.

7.2 Similar Polygons Similar figures – have the same shape but not necessarily the same size. You can abbreviate is similar to with the symbol ~ . Two.

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

Chapter 7 Quiz Review Lessons

Congruent Polygons Sec 6.5 GOALS: To identify congruent polygons.

Solve the following proportions. a = 9 b = 7 c = 6 d = ±6.

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

Geometry Section 8.3 Similar Polygons. In very simple terms, two polygons are similar iff they have exactly the same shape.

SIMILAR AND CONGRUENT POLYGONS LESSON 35POWER UP GPAGE 229.

8.3 Similar Polygons. Similar Polygons Definition : Similar polygons have congruent angles and sides in the same ratio (called Scale factor). Write the.

Ms. Drake 7th grade Math Fractions Lesson 44 Similar Figures and Proportions.

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

Triangle Similarity: Angle Angle. Recall Recall the definitions of the following: Similar Congruent Also recall the properties of similarity we discussed.

7-2 Similar Polygons Objectives Students will be able to:

Warm-Up If ∆QRS  ∆ZYX, identify all 3 pairs of congruent angles and all 3 pairs of congruent sides.

Unit 1 Transformations Day 5.  Similar Polygons - Two figures that have the same shape but not necessarily the same size ◦ Symbol: ~ ◦ Similar Polygons.

8.1 Similar Polygons OBJ: SWBAT use similarity statements, find corresponding lengths and perimeter and areas of similar polygons and decide whether polygons.

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

 Two polygons are similar polygons if corresponding angles are congruent and if the lengths of corresponding sides are proportional.

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.

Sec. 6–2 Similar Polygons. Figures that are similar (~) have the same shape but not necessarily the same size. Angles are congruent, Sides are proportional.

Ratios in similar polygons

Corresponding Parts of Similar Triangles

7.4 Showing Triangles are Similar: SSS and SAS

Objective To identify and apply similar polygons

EQ: How do you identify similar polygons?

Similarity Postulates

7.1 Proportions Solving proportions

Similar Polygons.

7-2 Similar Polygons.

Date: Topic: Similar Polygons (7.4)

6.3 Use Similar Polygons.

Y. Davis Geometry Notes Chapter 7.

5.3 Proving Triangle Similar

Chapter 6.3 Notes: Use Similar Polygons

Z Warm Up W U 5 V X Y 6 XYZ 5/

Chapter 2 Similarity and Dilations

7-3 Similar Triangles.

SIMILAR POLYGONS Two figures are similar if

5.3 Proving Triangle Similar

Z Warm Up W U 5 V X Y 6 XYZ 5/

7-3 Proving Triangles Similar

Proving Triangles Similar.

Similar Figures.

6-1: Use Similar Polygons

Secondary Math 2 8.3/8.4 – Similarity

Section 7-3 Similar Polygons.

Corresponding Parts of Similar Triangles

Proving Triangles Similar.

Parts of Similar Triangles

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

6-3/6-4: Proving Triangles Similar

Z Warm Up W U 5 V X Y 6 XYZ 5/

6.3 Using Similar Triangles

Chapter 7 Similarity.

Unit 2 Similarity, Congruence, and Proofs

8.4 Similar Triangles This can be written from the similarity statement (without even looking at the picture!) In similar polygons, all corresponding angles.

7.2 : Similar Polygons Similar polygons have:

Presentation transcript:

Use Similar Polygons & AA Postulate 6.3 & 6.4 Use Similar Polygons & AA Postulate

SIMILAR POLYGONS Similar Polygons-Same Shape Corresponding angles are congruent Corresponding side lengths are proportional

List all pairs of congruent angles List all pairs of congruent angles. Write the ratios of the corresponding sides.

EXAMPLE List all pairs of congruent angles. Write the ratios of corresponding sides in a statement of proportionality.

Scale Factor If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor.

Determining Similarity Determine whether the polygons are similar. If they are similar, find the scale factor.

Determine whether the polygons are similar Determine whether the polygons are similar. If they are similar, find the scale factor.

Determine whether the polygons are similar Determine whether the polygons are similar. If they are similar, find the scale factor.

Perimeters of Similar Polygons Perimeter: Sum of the sides of a polygon Ratio of the perimeters = Ratio of corresponding sides Ratio of corresponding lengths=scale factor Altitudes, Medians, Angle Bisectors…

Find the scale factor of the polygon on the left to the one on the right. Find the perimeter of each polygon.

Find the scale factor of the polygon on the left to the one on the right. Find the perimeter of each polygon.

Are the two triangles similar? What do we need to know? Corresponding angles are congruent All corresponding sides have the same proportion Would a simpler way be nice?

Angle-Angle Triangle Similarity If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. This can only be used for triangles!

Determine whether the triangles are similar Determine whether the triangles are similar. If yes, write the similarity statement.

Determine whether the triangles are similar Determine whether the triangles are similar. If yes, write the similarity statement. 1. 2.

Indirect Measurement When given similar triangles, write a proportion to find missing side lengths.