Geometry 4-7 Complete Lesson: Congruence in Overlapping Triangles
By Matt Richardson
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Last updated about 3 years ago
26 Questions
Note 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.
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Question 1
1.
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.
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Question 2
2.
Take Note: Define common angle (in overlapping triangles). On the canvas, sketch a pair of overlapping triangles and label a common angle.
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Question 3
3.
Take Note: Define common side (in overlapping triangles). On the canvas, sketch a pair of overlapping triangles and label a common side.
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Question 4
4.
Problem 1 Got It?
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Question 5
5.
Problem 1 Got It?
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Question 6
6.
Problem 2 Got It? Complete the proof on the canvas.
You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.
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Question 7
7.
Problem 3 Got It? Complete the proof on the canvas.
You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.
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Question 8
8.
Problem 4 Got It? Complete the proof on the canvas.
You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.
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Question 9
9.
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Question 10
10.
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Question 11
11.
Separate and redraw the overlapping triangles. Label the vertices.
You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.
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Question 12
12.
Separate and redraw the overlapping triangles. Label the vertices.
You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.
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Question 13
13.
Reasoning: In Exercise 1, both triangles have vertices J and K. Are ∠J and ∠K common angles for △MKJ and △LJK? Explain. You may also use the canvas to help illustrate your explanation.
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Question 15
15.
Reasoning: In the figure, which pair of triangles could you prove congruent first in order to prove that △ACD ≅ △CAB ? Explain. You may also use the canvas to help illustrate your explanation.
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Question 16
16.
Enter only the word that fills the blank, with no spaces.
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Question 17
17.
Enter only the word that fills the blank, with no spaces.
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Question 18
18.
Enter only the word that fills the blank, with no spaces.
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Question 19
19.
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Question 20
20.
Review Lesson 3-6: Complete the construction using the GeoGebra geometry utility (embedded below or at geogebra.org/geometry). 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.
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Question 21
21.
Review Lesson 1-7: Find the coordinates of the midpoint of the segment with the given endpoints.
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Question 22
22.
Review Lesson 1-7: Find the coordinates of the midpoint of the segment with the given endpoints.
Enter your response in this format, no spaces: (-3.5,14).
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Question 23
23.
Review Lesson 1-7: Find the coordinates of the midpoint of the segment with the given endpoints.
Enter your response in this format, no spaces: (-3.5,14).
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Question 24
24.
Vocabulary Review: Identify the common side of each pair of triangles.
\overline{RP}
\overline{AB}
\overline{ZY}
\overline{RT}
\overline{WX}
\overline{WY}
\overline{AC}
△ABC and △ADC
△XWZ and △YWZ
△RST and △RPT
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Question 25
25.
Use Your Vocabulary: Refer to the diagram and identify the common regions of the overlapping figures named on the right.
