Geometry 4-6 Congruence in Right Triangles

by Matthew Richardson

| 24 QuestionsNote from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

1

2

1

5

Solve It! One of the tent flaps was damaged in a storm. Can you use the other flap as a pattern to replace it?

Yes

No

2

10

Explain.

3

20

Problem 1 Got It? Complete the proof on the canvas.

4

10

Problem 1 Got It? Reasoning: Your friend says, "Suppose you have two triangles with congurent hypotenuses and one pair of congruent legs. It does not matter which leg in the first triangle is congruent to which leg in the second triangle. The triangles will be congruent." Is your friend correct? Explain.

5

20

Problem 2 Got It? Complete the proof on the canvas.

6

6

10

A

B

C

D

7

7

10

A

B

C

D

8

8

10

A

B

C

D

9

9

10

A

B

C

D

10

5

Vocabulary: A right triangle has side lengths of 5 cm, 12 cm, and 13 cm. What is the length of the hypotenuse?

5 cm

12 cm

13 cm

11

10

Vocabulary: Explain how you identified the hypotenuse in the previous item.

12

10

Compare and Contrast: How do the HL Theorem and the SAS Postulate compare? How are they different? Explain.

13

14

13

10

Error Analysis: Your classmate says that there is not enough information to determine whether the two triangles shown are congruent. Is your classmate correct?

Yes

No

14

10

Explain.

15

5

Review Lesson 4-5: Consider the congruence statement.

What type of triangle must △STU be?

Consider sketching △STU and labeling all known information.

isosceles

equilateral

scalene

16

5

Review Lesson 4-5: Consider the congruence statement.

What type of triangle must △STU be?

Consider sketching △STU and labeling all known information.

isosceles

equilateral

scalene

17

17

10

Review Lessons 4-3 & 4-6: Can you conlude that the triangles are congruent? Explain.

No, they're not or there is not enough information.

Yes, they're congruent by SSS.

Yes, they're congruent by SAS.

Yes, they're congruent by AAS.

Yes, they're congruent by ASA.

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5

Vocabulary Review: True or False? Segments that are congruent have the same length.

True

False

19

5

Vocabulary Review: True or False? Polygons that are congruent have the same shape but are not always the same size.

True

False

20

5

Vocabulary Review: True or False? In congruent figures, corresponding angles have the same measure.

True

False

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22

23

21

5

right

congruent

22

5

right

congruent

23

5

right

congruent

24

10

Reflection: Math Success

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