Similar Triangles Quizziz

Right Triangle Altitude/ Similarity Theorem Proof:

Given: Right triangle ABC, with CD the altitude to the hypotenuse.

Prove: ΔABC ~ ΔACD ~ ΔCBD.

1. 1. Both smaller triangles, ΔACD and ΔCBD, are __________ triangles.

1. 2. Both △ACD and △CBD share _________________ with △ABC.

2. 3. △ACD and △ABC share _______________.

3. 4. △CBD and △ABC share _______________.

4. 5. So, each smaller triangle is similar by the ________________________.

5. 6. Since both △ACD and △CBD are similar to △ABC, corresponding angles are congruent.

6. 7. So, △ABC ~ △ACD ~ △CBD

• 1. 1. similar

  2. 2. sides

  3. 3. angle A

  4. 4. angle C

  5. 5. transitive property

• 1. 1. right

  2. 2. angles

  3. 3. angle A

  4. 4. angle C

  5. 5. transitive property

• 1. 1. right

  2. 2. sides

  3. 3. angle B

  4. 4. angle C

  5. 5. substitution property

• 1. 1. right

  2. 2. angles

  3. 3. angle A

  4. 4. angle C

  5. 5. substitution property

Tags

CCSS.HSG.SRT.B.4

Triangle ABC is transformed to create Triangle A'B'C'. Describe the sequence of transformations needed to create A'B'C'.

• 1. 1. Dilate by scale factor > 1

  2. 2. Reflect across AC

  3. 3. Reflect horizontally across point A

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

Create a proportion that justifies the image shown.

Tags

CCSS.HSG.SRT.A.2

Determine if the triangles are similar. If so, identify the similarity theorem that shows it.

• SSS

• AA

• SAS

• Not Similar

Tags

CCSS.HSG.SRT.B.5

Tags

CCSS.HSG.CO.C.9

Dimitri wants to measure the height of the palm of a tree. He lines himself up with the palm tree’s shadow so that the tip of his shadow meets the tip of the palm tree’s shadow. Then, he asks a friend to measure the distance from where he was standing to the tip of his shadow and the distance from the palm tree to the tip of its shadow. What is the height of the palm tree?

Tags

CCSS.HSG.SRT.B.5

Determine the midpoint of (6,-3) and (-4, 5).

Tags

CCSS.HSG.GPE.B.6

Determine the value of x in the diagram. Write which theorem you used to solve.

• Right Triangle Similarity Theorem

• Right Triangle Altitude Theorem

• Right Triangle Leg Theorem

• 10

• 15

Tags

CCSS.HSG.CO.C.9

Triangle KEF is similar to Triangle KLM. Determine the value of x.

• 11

• 13

• 18

• 21

Tags

CCSS.HSG.SRT.A.2

Triangle ABC is similar to triangle FGH. Determine the length of GH.

• 20 cm

• 22.5 cm

• 25.5 cm

• 30 cm

Tags

CCSS.HSG.SRT.A.2