S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the...

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Similar Polygons

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Congruent ≅ sides and angles are exactly the same. Similar ∼ angles are exactly the same but the sides are proportional Similar figures have a similarity ratio. This is the ratio of the lengths of two corresponding sides. The order in a ratio matters and it must be in the form of a simplified fraction.

Transcript of S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the...

Page 1: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

Similar Polygons

Page 2: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

Warm Up1. If ∆QRS ∆ZYX, identify the pairs of congruent angles and the pairs of congruent sides.Solve each proportion.

2. 3.

Page 3: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

Congruent ≅ sides and angles are exactly the same.

Similar ∼ angles are exactly the same but the

sides are proportionalSimilar figures have a similarity ratio. This is the ratio of the lengths of two

corresponding sides. The order in a ratio matters and it must be in the

form of a simplified fraction.

Page 4: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

Figures that are similar (~) have the same shape but not necessarily the same size.

Page 5: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

A similarity ratio is the ratio of the lengths of

the corresponding sides of two similar polygons.

The similarity ratio of ∆ABC to ∆DEF is , or .

The similarity ratio of ∆DEF to ∆ABC is , or 2.

Page 6: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

1. Are the two polygons similar?

2. Find the similarity ratio of ABCD to EFGH.

3. Find the similarity ratio of EFGH to ABCD.

Page 7: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

1. What is the similarity ratio of the two similar polygons?

Find x and y.

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Page 8: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

True or false If two figures are congruent, they are always

similar.

If two figures are similar, they are always congruent.

The similarity ratio of congruent figures is 1 to 1.

Page 9: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.
Page 10: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.
Page 11: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.
Page 12: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

The following polygons are similar.Find the Similarity ratio of small to bigFind the value of x.

Page 13: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

Find the length of the model to the nearest tenth of a centimeter.

Page 14: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

Lesson Quiz: Part I1. Determine whether the polygons are similar. If so, write the

similarity ratio and a similarity statement.

2. The ratio of a model sailboat’s dimensions to the actual boat’s dimensions is . If the length of the model is 10 inches, what is

the length of the actual sailboat in feet?

3. Tell whether the following statement is sometimes, always, or never true. Two equilateral triangles are similar.

Page 15: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

Homework

Page 16: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.
Page 17: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.
Page 18: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.
Page 19: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.
Page 20: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.
Page 21: S IMILAR P OLYGONS. Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3.

Chapter 4: Congruent Triangles - West Jefferson Local ... Glencoe 2003 ch… · For Lessons 4-2, 4-4, and 4-5 Congruent Angles Name the indicated angles or pairs of angles if p q

Chapter 4: Congruent Triangles - West Jefferson Local ... Glencoe 2003 ch… · For Lessons 4-2, 4-4, and 4-5 Congruent Angles Name the indicated angles or pairs of angles if p q

Quadrilaterals. Parallelogram quadrilateral with 2 pairs of parallel sides Opposite sides are congruent. Opposite angles are congruent. The diagonals.

Quadrilaterals. Parallelogram quadrilateral with 2 pairs of parallel sides Opposite sides are congruent. Opposite angles are congruent. The diagonals.

Congruent Triangles Introduction to congruent angles.

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2....3 Corresponding sides: Corresponding angles: K M LP R Q •Triangles are congruent if all pairs of corresponding angles are congruent and all pairs of corresponding sides Title

 · Parallel Lines and Angle Pairs When two parallel lines are cut by a transversal, the following pairs of angles are congruent. corresponding angles

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Holt Geometry 7-2 Ratios in Similar Polygons Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve.

Holt Geometry 7-2 Ratios in Similar Polygons Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve.

Geometry Day 4 Notes Proving Triangles Congruent · In Lesson 4.1, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are

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ch 4.pdfExploring Congruent Triangles When two figures have exactly the same shape and size, they are said to be congruent. For two congruent triangles there are three pairs of corresponding

ch 4.pdfExploring Congruent Triangles When two figures have exactly the same shape and size, they are said to be congruent. For two congruent triangles there are three pairs of corresponding

1.cdn.edl.io · Explain your answer. Plan What should you look for first, sides or angles? Start with sides. If you have three pairs of sides congruent, use SSS. ... wo pairs of corresponding

1.cdn.edl.io · Explain your answer. Plan What should you look for first, sides or angles? Start with sides. If you have three pairs of sides congruent, use SSS. ... wo pairs of corresponding

When we talk about congruent triangles, we mean everything about them is congruent (or exactly the same) (or exactly the same) All 3 pairs of corresponding.

When we talk about congruent triangles, we mean everything about them is congruent (or exactly the same) (or exactly the same) All 3 pairs of corresponding.

1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides.…

1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides.…

Sasha Vasserman. Two triangles are similar if two pairs of corresponding angles are congruent.

Sasha Vasserman. Two triangles are similar if two pairs of corresponding angles are congruent.

4.1 Congruent Figures-Reading and CCmitchelldtech.weebly.com/uploads/3/7/5/6/37567383/4.1_congruent... · pairs are congruent, then the triangles are congruent. SHOW SOLUTION GOT

4.1 Congruent Figures-Reading and CCmitchelldtech.weebly.com/uploads/3/7/5/6/37567383/4.1_congruent... · pairs are congruent, then the triangles are congruent. SHOW SOLUTION GOT

Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3. x = 9x = 18 Q Z;

Warm Up 1. If ∆ QRS ∆ ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2. 3. x = 9x = 18 Q Z;

List all pairs of congruent angles, and write a · List all pairs of congruent angles, and write a proportion that relates the corresponding sides for each pair of similar polygons.

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5 Congruent Triangles - Big Ideas · PDF file5.2 Congruent Polygons ... no congruent sides at least 2 congruent sides 3 congruent sides ... 238 Chapter 5 Congruent Triangles