Review of Lesson 2 - Similar Polygons

1

Find the scale factor of
to
.

1

. Find the scale factor of MNPQ to RSTU.

1

Find the values of x, y, and z.

x =

y =

z = degrees

1

Find the value of
Round to nearest tenth.

1

Is the BLUE polygon similar to the RED polygon?

Yes. They are similar.

No. They are NOT similar.

1

Explain your reasoning/rationale for why the BLUE and RED polygons are similar or NOT similar.

Sample Answer: The polygons are NOT similar. Although the sides are proportional (2:1 ratio), the corresponding angles are NOT congruent.

1

Is the BLUE polygon similar to the RED polygon?

Yes. They are similar.

No. They are NOT similar.

1

Explain your reasoning/rationale for why the BLUE and RED polygons are similar or NOT similar.

Sample Answer: The BLUE and RED triangles are SIMILAR because

ALL 3 pairs of corresponding angles are congruent
AND
ALL 3 side ratios are EQUAL (1:2) --> sides are PROPORTIONAL

1

Are the two polygons similar?

Yes. They are similar.

No. They are NOT similar.

1

Explain your reasoning/rationale for why the polygons are similar or NOT similar.

Sample Answer:

No they are NOT similar.

Although ALL pairs of corresponding angles are congruent, the corresponding side lengths ARE NOT proportional. The long sides are in a 1:2 ratio while the short sides are in a 4:9 ratio.

Lesson 3 : Proving Triangles Similar

There are 3 WAYS to Prove Triangles SIMILAR

Angle - Angle (AA)
Side-Side-Side (SSS of Similarity )
Side-Angle-Side (SAS of Similarity)

Note: If two angles of one triangle are congruent to two angles of a second triangle, then the THRIRD angles MUST be congruent (Third Angle Theorem).

Even though you will be able to prove all three corresponding angle pairs congruent, you only need to show/prove TWO pairs.

1

Are the two triangles similar by Angle-Angle Similarity?

Yes.

by A.A. Similarity

No. Triangles are NOT similar.

1

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

1

Are the two triangles similar by Angle-Angle Similarity?

Yes.

by A.A. Similarity

No. The triangles are NOT similar.

1

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

1

Are the two triangles similar by Angle-Angle Similarity?

Yes.

by A.A. Similarity

No. The triangles are NOT similar

1

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Simply stated, if you can show that ALL THREE side ratios are equal, you can then state the triangles are SIMILAR.

If the shortest side ratio = middle side ratio = longest side ratio, then the triangles are SIMILAR

1

Are the two triangles similar by Side-Side-Side Similarity?

Yes.

by SSS Similarity

No. The triangles are NOT similar.

1

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

1

Are the two triangles similar by Side-Side-Side Similarity?

Yes.

by SSS Similarity.

No. The triangles are NOT congruent.

1

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

1

Are the two triangles similar by Side-Side-Side Similarity?

Yes.

by SSS Similarity

No. The triangles are NOT similar.

1

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

null

Simply stated, show TWO corresponding sides ratios are EQUAL

AND

ONE pair of angles CONGRUENT****

****The angle pair MUST be the angles formed/included(between) by the sides that are proportional

1

Are the two triangles similar by Side-Angle-Side Similarity?

Yes.

by SAS Similarity

No. The triangles are NOT similar.

1

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

1

Are the two triangles similar by Side-Angle-Side Similarity?

Yes.

by SAS similarity

No. The triangles are NOT similar.

1

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

1

Are the two triangles similar by Side-Angle-Side Similarity?

Yes.

by SAS similarity.

No. The triangles are NOT similar.

1

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

1

Are the two triangles similar by Side-Angle-Side Similarity?

Yes.

by SAS similarity.

No. The triangles are NOT similar.

1

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Similar Triangle Proofs (2- column)

Definition of Similar Triangles (Polygons)

null

1

Write a Two Column Formal Proof

1

Write a Two Column Proof

Using Similar Triangles as a Tool of Indirect Measurement

Sometimes you can use similar triangles to find distances and lengths that are difficult to measure directly. This is called INDIRECT MEASUREMENT.

Key for these types of problems:

Draw pretty pictures.
Okay to make some assumptions. For example, a building/tree/person/mountain "meets"/intersects a ground at a right angle.

1

Mr. Met is 6 feet tall (mostly his GINORMOUS head) and is standing 10 feet from a tree. Mr. Met is standing perfectly in the shadow of the tree (meaning Mr. Met's and the tree's shadow end at the SAME spot). He casts an 11 foot shadow. How tall is the tree to the nearest tenth of a foot?

Lesson 3 Proving Triangles Similar

Review of Lesson 2 - Similar Polygons

Lesson 3 : Proving Triangles Similar

Similar Triangle Proofs (2- column)

Definition of Similar Triangles (Polygons)

MORE PROBLEMS

Lesson 3 Proving Triangles Similar

Review of Lesson 2 - Similar Polygons

Find the scale factor of to .

. Find the scale factor of MNPQ to RSTU.

Find the value of Round to nearest tenth.

Is the BLUE polygon similar to the RED polygon?

Explain your reasoning/rationale for why the BLUE and RED polygons are similar or NOT similar.

Is the BLUE polygon similar to the RED polygon?

Explain your reasoning/rationale for why the BLUE and RED polygons are similar or NOT similar.

Are the two polygons similar?

Explain your reasoning/rationale for why the polygons are similar or NOT similar.

Lesson 3 : Proving Triangles Similar

Are the two triangles similar by Angle-Angle Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Angle-Angle Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Angle-Angle Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Side-Side-Side Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Side-Side-Side Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Side-Side-Side Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Side-Angle-Side Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Side-Angle-Side Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Side-Angle-Side Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Side-Angle-Side Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Similar Triangle Proofs (2- column)

Definition of Similar Triangles (Polygons)

Write a Two Column Formal Proof

Write a Two Column Proof

Using Similar Triangles as a Tool of Indirect Measurement

Sometimes you can use similar triangles to find distances and lengths that are difficult to measure directly. This is called INDIRECT MEASUREMENT.

Mr. Met is 6 feet tall (mostly his GINORMOUS head) and is standing 10 feet from a tree. Mr. Met is standing perfectly in the shadow of the tree (meaning Mr. Met's and the tree's shadow end at the SAME spot). He casts an 11 foot shadow. How tall is the tree to the nearest tenth of a foot?

MORE PROBLEMS

What are the two triangles similar by?

What are the two triangles similar by?

What are the two triangles similar by?

What are the two triangles similar by?

What are the two triangles similar by?

What are the two triangles similar by?

What are the two triangles similar by?

What are the two triangles similar by?

What are the two triangles similar by?

What are the two triangles similar by?

What are the two triangles similar by?

To find the distance across a pond from point B to point C, a surveyor drew the diagram below. The measurements he made are indicated on his diagram.Use the surveyor's information to determine and state the distance from point B to point C, to the nearest yard.

Write a two-column formal proof.

Write a two-column proof.

Write a two-column proof.

Write a two-column proof.

Write a two-column proof.

Find the scale factor of to .

. Find the scale factor of MNPQ to RSTU.

Find the value of Round to nearest tenth.

Is the BLUE polygon similar to the RED polygon?

Explain your reasoning/rationale for why the BLUE and RED polygons are similar or NOT similar.

Is the BLUE polygon similar to the RED polygon?

Explain your reasoning/rationale for why the BLUE and RED polygons are similar or NOT similar.

Are the two polygons similar?

Explain your reasoning/rationale for why the polygons are similar or NOT similar.

Are the two triangles similar by Angle-Angle Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Angle-Angle Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Angle-Angle Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Are the two triangles similar by Side-Side-Side Similarity?

Explain your rationale/reasoning to your answer for the why the two triangles are similar or NOT SIMILAR.

Find the scale factor of
to
.

Find the value of
Round to nearest tenth.

To find the distance across a pond from point B to point C, a surveyor drew the diagram below. The measurements he made are indicated on his diagram.
Use the surveyor's information to determine and state the distance from point B to point C, to the nearest yard.

Find the scale factor of
to
.

Find the value of
Round to nearest tenth.

To find the distance across a pond from point B to point C, a surveyor drew the diagram below. The measurements he made are indicated on his diagram.
Use the surveyor's information to determine and state the distance from point B to point C, to the nearest yard.