Complete the following proof. Match the number with the correct piece of missing information. K Given: ZK E ZM M. Prove: JK PM Reason Statement LK ZM 1. Given ML LK 2. ZJLK LPLM 3. A MLPA KLJ 4. JK PM

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Complete the following proof. Match the number with the correct piece of missing information.**

![Diagram of triangles]  
A geometric diagram is shown with two triangles: ∆MLP and ∆KLJ. Lines ML and LK are given as congruent.

**Given:**

∠K ≅ ∠M

**Prove:**

JK ≅ PM

| Statement                  | Reason     |
|----------------------------|------------|
| ∠K ≅ ∠M                    | Given      |
| ML ≅ LK                    | 1.         |
| ∠JLK ≅ ∠PLM               | 2.         |
| ∆MLP ≅ ∆KLJ               | 3.         |
| JK ≅ PM                    | 4.         |

1. ML ≅ LK (Given)
2. ∠JLK ≅ ∠PLM (Given or properties of transversals/alternate interior angles)
3. ∆MLP ≅ ∆KLJ (ASA or AAS criteria)
4. JK ≅ PM (CPCTC - Corresponding Parts of Congruent Triangles are Congruent)
Transcribed Image Text:**Complete the following proof. Match the number with the correct piece of missing information.** ![Diagram of triangles] A geometric diagram is shown with two triangles: ∆MLP and ∆KLJ. Lines ML and LK are given as congruent. **Given:** ∠K ≅ ∠M **Prove:** JK ≅ PM | Statement | Reason | |----------------------------|------------| | ∠K ≅ ∠M | Given | | ML ≅ LK | 1. | | ∠JLK ≅ ∠PLM | 2. | | ∆MLP ≅ ∆KLJ | 3. | | JK ≅ PM | 4. | 1. ML ≅ LK (Given) 2. ∠JLK ≅ ∠PLM (Given or properties of transversals/alternate interior angles) 3. ∆MLP ≅ ∆KLJ (ASA or AAS criteria) 4. JK ≅ PM (CPCTC - Corresponding Parts of Congruent Triangles are Congruent)
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