Congruent/Similar Triangles

Theorems

100

This theorem states that triangles are similar if all of the corresponding sides are equal.

What is SSS (side-side-side)

200

This theorem says that triangles are similar if two pairs of corresponding sides of two triangles are proportional and the included angle are congruent.

What is SAS (side-angle-side) Similarity Theorem

300

This theorem states that if two angles of one triangle are congruent to the corresponding angles of another triangle then the triangles are similar.

What is AA (Angle-angle) Similarity Theorem

400

This theorem states that triangles are congruent if two corresponding angles and the included side are the same.

What is ASA Congruency Thm.

500

This theorem states that triangles are congruent if two corresponding angles and the non-included side are the same.

What is AAS Congruency Theorem

USING Similar triangles

100

 Triangle A has side lengths of 3 cm, 4 cm, and 5 cm. Triangle B is similar to Triangle A, but it is an enlargement with a scale factor of 3. What are the side lengths of Triangle B?

 The side lengths of Triangle B are 9 cm, 12 cm, and 15 cm.

200

How tall is the flagpole? You want to know the height of a flagpole by measuring with a mirror. If you place the mirror 10 feet from the flagpole and then you go and stand another 5 feet from the mirror. You are 6 feet tall. Draw similar triangles depicting this situation.

12 feet.

300

A 2ft tall statue stands next to a baby elephant casting a 3 foot shadow. If the baby elephant casts a shadow that is 12ft long, then how tall is the elephant?

What is 8 feet tall

400

You are trying to estimate the height of a tree but you do not have measuring tape that long. So you are going to indirectly measure it. You are 5.5 feet tall and right now have a 4 foot shadow. The tree currently has a shadow of 6 feet. How tall is the tree?

What is 8 1/4 ft or 8 ft 3 in or 8.25

500

You have a triangle with sides 14, 21 and 28. Which of the following are lengths of a a similar triangle? A. 15,15, 25 B. 24,30,36 C.18, 27, 36 D.21, 28, 35

What is C.18, 27, 36

Find the missing piece

100

What is the length of all sides? Picture 1

FG=8

FH=13

GH=16

200

What are the angles? Are they similar? By what postulate? Picture 2

angle a = 69

angle b = 56

angle d = 69

angle e = 56

similar by AA

300

Picture 4. What is h? What is the scale factor of the tree to the smaller triangle?

h=3.1

k = 1/2.8

400

Find the side length, determine if congruent or similar. PIC 5

Angle D = 49

Angle D = 49

DA = 6

DC = 6

congruent

500

Find the lengths, determine if similar or congruent. Picture 3

FE = 16

FD = 31

ED = 12

 congruent

Are they or not?

100

Are these triangles similar or congruent? Which theorem? Picture 6

SAS congruent

200

Are these triangles similar? What is the length of CD, BA, and BE. Which Theorem? Picture 7

BC/ED = 8/16 = 1/2

BA = 1/2 x 28 = 14 cm

CA/DA = 1/2 (this is k)

DA = 10/ (1/2) = 20 

CD = DA - CA = 20-10 = 10

yes similar by AA

300

Picture 9 Are these triangles similar? Which Theorem?

AA 

Angle ABC = Angle DEC

AC/DC = 8/x

BC/EC = 6/15 = 2/5 (small to big)

AC/DC = 2/5 = 8/DC

DC = 8x5/2 = 20 

400

Are these triangles similar? Which Theorem? Picture 8

No, the sides/angles do not correspond to each other. The only corresponding angle is 76. The internal angles are right but not proportionate.

500

Are these triangles similar or congruent or both or neither? Which Theorem(s)? What are ALL the missing side lengths. Picture 10

Similar SSS postulate (3 sides given, the rest found out through proportion)

6/x = 10/8

4.8 = x

Triangle DFG 

8/10 = y/8 

6.4 = y

Triangle EFD 

6/8 = z/4.8

3.6 = z

Congruency vs Similarity

100

Two triangles are similar by the AA theorem can they also be assumed to be congruent?

No, there is not enough information

200

Fact or Fiction: Congruent triangles are always similar triangles

What is OF COURSE---TRUE!

300

Main difference between similar triangles and congruent triangles.

What is similar triangles can have sides that are proportional and not the same length.

400

Two triangles have angle measurements of A=45, B=50, C=85 and D=45, E=50, F=85 Are these similar/congruent/both/neither

What is similiar

500

Triangles that are found similar by this theorem are also congruent.

What is SSS.....If all sides are the same then the triangles are similar and congruent