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Similar triangles packet

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Bachelor of Secondary Education Major in English (BSED ENGLISH 3)

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Southern Masbate Roosevelt College

Academic year: 2024/2025

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Unit 5

Similar

Triangles

Lesson: Similar Triangles

Just as congruence introduced us to new notation, similarity will have its own set of notation.

If ΔCAT is congruent to ΔMEW, we write CAT  MEW two polygons are similar we use the symbol that sits above the equal sign in the congruent symbol: ~.

For example, the statement CORN~ PEAS says that quadrilateral CORN is similar to quadrilateral PEAS. Just as in statements of congruence, the order of the letters tells you which segments and which angles in the two polygons correspond.

Corresponding angles are congruent:

Corresponding segments are proportional:

The ratio of the lengths of any two segments in one polygon is equal to the ratio of the

corresponding two segments in the similar polygon. For example, CO PE OR EA

 orNR SA CO PE



As we know, Similar Figures have the same shape, but not necessarily the same size.

All corresponding angles are equal and corresponding sides are proportional. Proportionality is based on a scale factor which we will see later in transformation (dilations).

Guided Practice

Directions: Use the similarity statement to solve for x.

Δ𝑈𝑇𝑉~~Δ𝐿𝐾𝑀 2. Δ𝑈𝑉𝑊~~Δ𝑀𝐾𝐿

Skills Practice: Similar Triangles

Directions: Given the similarity statement, solve for the missing variable.

Δ𝐶𝐷𝐸~~Δ𝑈𝑇𝑆 2. Δ𝑆𝑅𝑇~~Δ𝐵𝐶𝐴

3. Δ𝑅𝑆𝑄Δ𝐷𝐸𝐶 4. Δ𝑅𝑆𝑄Δ𝐺𝐹𝐻

5. Δ𝐿𝐾𝑀Δ𝑄𝑃𝑅 6. Δ𝐺𝐻𝐹Δ𝑉𝑊𝑈

7. Δ𝐽𝐾𝐿Δ𝐽𝐶𝐷 8. Δ𝑄𝑅𝑆Δ𝑁𝑀𝐿

Additional Practice- Similar Triangles

Triangle ABC is similar to triangle PQR. Write a proportion that can be used to find n. Then solve for n.
Given ABC DEF,circle the following true proportions/statements.

AB AC

DE EF

 AC BC

DF EF

 AB BC

AC EF

 BC CB

DF EF



C  F A  E C  D A  D

Triangle MNO and PQR are similar

a. List corresponding angles

b. List the ratios of corresponding sides.

Warm Up

Triangles ABC and DEF are similar.

a. List the ratios of corresponding sides.

b. Find the lengths of the missing sides.

Triangles GHI and JKL are similar.

a. List the ratios of corresponding sides.

b. Find the lengths of the missing sides.

c. Find the measures of the missing angles.

Angle- Angle AA~

Statement: ________________

Guided Practice:

Directions: Show that the following triangles are similar, by showing either angles congruent or sides proportional. Next state the similarity statement.

1. 2.

Show corresponding parts: Show corresponding parts:

Circle: AA , SSS , SAS Circle: AA , SSS , SAS

Statement: ABC ______ Statement: GHJ ______

3.

Show corresponding parts:

Circle: AA , SSS , SAS

Statement: FHG ______

13

Homework- Similar Triangles

For questions 1 – 4 , write a similarity statement. Then find the measures of the missing sides.

16

Which of the following is true about the triangles below?

A. Similar but not congruent B. Congruent but not similar C. Both similar and congruent D. Neither similar nor congruent

Which of the following is true about the triangles below?

A. Similar but not congruent B. Congruent but not similar C. Both similar and congruent D. Neither similar nor congruent

SAT Prep: A summer camp counselor wants to find a length, x, in feet across a lake as represented in the sketch below. The lengths represented by AB, EB, BD, and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet respectively. Segments AC and DE intersect at B, and AEBand CDBhave the same measure. What is the value of x?

17

Identify which property will prove these triangles are similar (AA similarity, SAS similarity, SSS similarity)

19

Lesson: Similar Triangle Proofs

Complete the given two-column proofs.

Given NO MO QO PO Prove:MNO ~PQO
Given:MQ|| OP Prove:MNQ ~PON

Statements Reasons

20

Given:AE ||BD Prove:ACE ~BCD
Given DABand DCAare right triangles

Prove: DAB ~ DCA Statements Reasons

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