E P -10 2

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Activity 1:**

**Recall:**

Any object will keep the same shape and size after a rigid transformation. Properties preserved under rigid motions include segment lengths and angle measures.

**Diagram Description:**

The image contains a coordinate plane with several triangles. 

1. **Triangle A** (Green):
   - Vertices: A (-9, 0), B (-10, -3), C (-7, -3)
   - Enclosed by a green shaded area.

2. **Triangle D** (Blue):
   - Vertices: E (-5, 3), M (-3, 6), D (-4, 0)
   - Located in the upper left quadrant.

3. **Triangle G** (Purple):
   - Vertices: F (-7, -4), L (-6, -2), G (-4, -4)
   - Located in the lower left quadrant.

4. **Triangle P** (Blue):
   - Vertices: R (3, 5), S (5, 4), P (4, 2)
   - Located in the upper right quadrant.

5. **Triangle N** (Blue):
   - Vertices: R (3, 5), O (0, 1), N (1, -1)
   - The largest among the blue triangles and central.

6. **Triangle J** (Purple):
   - Vertices: X (2, -4), O (5, -3), J (3, -4)
   - Located in the lower right quadrant.

**Tasks:**

1. **List all pairs of congruent triangles.** Be sure to include a list of the 3 corresponding parts that you can show are congruent. Justify your answer.

2. **Choose a pair of triangles that are not congruent.** Explain why.
Transcribed Image Text:**Activity 1:** **Recall:** Any object will keep the same shape and size after a rigid transformation. Properties preserved under rigid motions include segment lengths and angle measures. **Diagram Description:** The image contains a coordinate plane with several triangles. 1. **Triangle A** (Green): - Vertices: A (-9, 0), B (-10, -3), C (-7, -3) - Enclosed by a green shaded area. 2. **Triangle D** (Blue): - Vertices: E (-5, 3), M (-3, 6), D (-4, 0) - Located in the upper left quadrant. 3. **Triangle G** (Purple): - Vertices: F (-7, -4), L (-6, -2), G (-4, -4) - Located in the lower left quadrant. 4. **Triangle P** (Blue): - Vertices: R (3, 5), S (5, 4), P (4, 2) - Located in the upper right quadrant. 5. **Triangle N** (Blue): - Vertices: R (3, 5), O (0, 1), N (1, -1) - The largest among the blue triangles and central. 6. **Triangle J** (Purple): - Vertices: X (2, -4), O (5, -3), J (3, -4) - Located in the lower right quadrant. **Tasks:** 1. **List all pairs of congruent triangles.** Be sure to include a list of the 3 corresponding parts that you can show are congruent. Justify your answer. 2. **Choose a pair of triangles that are not congruent.** Explain why.
Expert Solution
Step 1

1.

(a)

When we observe figure shape form by ACKB is a Quadrilateral.

with AB II CK and BK II AC , AB=CK and BK=AC

In ABC and KCB           AB=KC        (Given)           AC=KB        (Given)           BC=BC        (Common side)Therefore,ABCKCB   By SSS Rule                BAC=BKC                 ABC=BCK                 ACB=CBKCongruent part of congruent Triangles are congruent.

 

 

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