Geometry 4-7 Congruence in Overlapping 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

1

10 pts

Solve It! An assignment for your graphic design class is to make a colorful design using triangles. How many triangles are in your design? Enter only a number.

2

2

10 pts

Problem 1 Got It?

A

B

C

D

3

3

10 pts

Problem 1 Got It?

A

B

C

D

4

20 pts

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

5

20 pts

Problem 3 Got It? Complete the proof on the canvas.

6

20 pts

Problem 4 Got It? Complete the proof on the canvas.

7

7

10 pts

A

B

C

D

8

8

10 pts

A

B

C

D

9

10 pts

Separate and redraw the overlapping triangles. Label the vertices.

10

10 pts

Separate and redraw the overlapping triangles. Label the vertices.

11

11

10 pts

Reasoning: In Exercise 1, both triangles have vertices J and K. Are ∠J and ∠K common angles for △MKJ and △LJK? Explain.

12

13

13

10 pts

Reasoning: In the figure, which pair of triangles could you prove congruent first in order to prove that △ACD ≅ △CAB ? Explain.

14

15

16

17

14

5 pts

Enter only the word that fills the blank, with no spaces.

15

5 pts

Enter only the word that fills the blank, with no spaces.

16

5 pts

Enter only the word that fills the blank, with no spaces.

17

5 pts

Side Angle Side

Angle Side Angle

Side Side Side

Hypotenuse Leg

18

20 pts

Review Lesson 3-6: Complete the construction using GeoGebra. Screenshot your final product and upload it to the canvas. Be sure to label all points and leave any evidence that indicates how you completed the task.

Draw a line p and a point M not on p. Then construct line n through M so that n is perpendicular to P.

You may leave lines and points unlabeled.

19

5 pts

Review Lesson 1-7: Find the coordinates of the midpoint of the segment with the given endpoints.

(-1, -2)

(2, 4)

(1, 2)

(3, 3)

20

5 pts

Review Lesson 1-7: Find the coordinates of the midpoint of the segment with the given endpoints.

Enter your response in this format, with the only space following the comma: (-3.5, 14)

21

5 pts

Review Lesson 1-7: Find the coordinates of the midpoint of the segment with the given endpoints.

Enter your response in this format, with the only space following the comma: (-3.5, 14)

22

10 pts

Vocabulary Review: Identify the common side of each pair of triangles.

- segment AB
- segment AC
- segment AD
- segment BC
- segment WZ
- segment WX
- segment WY
- segment ZY
- segment RP
- segment RS
- segment RT
- segment ST

- △ABC and △ADC
- △XWZ and △YWZ
- △RST and △RPT

23

10 pts

Use Your Vocabulary: Identify the common regions of the overlapping figures in the diagram above.

- △ABG
- △ACF
- △EHD
- △GHB
- △BEC
- △GDF

- △FGD and △CBE
- △BEC and △HED

24

10 pts

Reflection: Math Success

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