Decide whether JKLM is similar to NPRS. Explain your reasoning. 6 95 M 140 3 140° 9 12 60° 65° 65° 15 The sum of the angle measures in a quadrilateral is 265 ZP = 275 corresponding side length of the smaller quadrilateral. So, the side lengths are x 0. Using this fact, you can determine that the missing angle measures are = 275 congruent. Also, each side of the larger quadrilateral is 10 V similar to NPRS. X ° and X •. So, the corresponding angles of the quadrilaterals (are x times longer than the vv proportional. Therefore, JKLM is
Decide whether JKLM is similar to NPRS. Explain your reasoning. 6 95 M 140 3 140° 9 12 60° 65° 65° 15 The sum of the angle measures in a quadrilateral is 265 ZP = 275 corresponding side length of the smaller quadrilateral. So, the side lengths are x 0. Using this fact, you can determine that the missing angle measures are = 275 congruent. Also, each side of the larger quadrilateral is 10 V similar to NPRS. X ° and X •. So, the corresponding angles of the quadrilaterals (are x times longer than the vv proportional. Therefore, JKLM is
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![**Determine Whether JKLM is Similar to NPRS: Explanation and Reasoning**
**Problem Statement:**
Decide whether quadrilateral \( JKLM \) is similar to quadrilateral \( NPRS \). Explain your reasoning.
**Diagrams:**
1. **Quadrilateral JKLM:**
- Vertices: \( J, K, L, M \)
- \( \angle J = 60^\circ \)
- \( \angle K = 65^\circ \)
- \( \angle L = 140^\circ \)
- \( \angle M = 95^\circ \)
- Side Lengths: \( JK = 4 \), \( KL = 5 \), \( LM = 2 \), \( MJ = 3 \)
2. **Quadrilateral NPRS:**
- Vertices: \( N, P, R, S \)
- \( \angle N = 95^\circ \)
- \( \angle P = 65^\circ \)
- \( \angle R = 140^\circ \)
- \( \angle S = 60^\circ \)
- Side Lengths: \( NP = 12 \), \( PR = 15 \), \( RS = 9 \), \( SN = 6 \)
**Steps and Analysis:**
1. **Sum of the Angle Measures:**
- The sum of the angle measures in any quadrilateral is always \( 360^\circ \). Therefore:
\[
\angle J + \angle K + \angle L + \angle M = 60^\circ + 65^\circ + 140^\circ + 95^\circ = 360^\circ
\]
- Thus, the sum of the angle measures is correct.
2. **Corresponding Angles:**
- Corresponding angles between \( JKLM \) and \( NPRS \) are as follows:
- \( \angle J \) and \( \angle S \) are both \( 60^\circ \).
- \( \angle K \) and \( \angle P \) are both \( 65^\circ \).
- \( \angle L \) and \( \angle R \) are both \( 140^\circ \).
- \( \angle M \) and \( \angle N \) are both \( 95^\circ \).
- Therefore,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b3aeb85-845c-4897-8321-5d700bdd20c9%2Fb81ea218-b7c0-4def-af29-69b2b81486df%2F41hjld_processed.png&w=3840&q=75)
Transcribed Image Text:**Determine Whether JKLM is Similar to NPRS: Explanation and Reasoning**
**Problem Statement:**
Decide whether quadrilateral \( JKLM \) is similar to quadrilateral \( NPRS \). Explain your reasoning.
**Diagrams:**
1. **Quadrilateral JKLM:**
- Vertices: \( J, K, L, M \)
- \( \angle J = 60^\circ \)
- \( \angle K = 65^\circ \)
- \( \angle L = 140^\circ \)
- \( \angle M = 95^\circ \)
- Side Lengths: \( JK = 4 \), \( KL = 5 \), \( LM = 2 \), \( MJ = 3 \)
2. **Quadrilateral NPRS:**
- Vertices: \( N, P, R, S \)
- \( \angle N = 95^\circ \)
- \( \angle P = 65^\circ \)
- \( \angle R = 140^\circ \)
- \( \angle S = 60^\circ \)
- Side Lengths: \( NP = 12 \), \( PR = 15 \), \( RS = 9 \), \( SN = 6 \)
**Steps and Analysis:**
1. **Sum of the Angle Measures:**
- The sum of the angle measures in any quadrilateral is always \( 360^\circ \). Therefore:
\[
\angle J + \angle K + \angle L + \angle M = 60^\circ + 65^\circ + 140^\circ + 95^\circ = 360^\circ
\]
- Thus, the sum of the angle measures is correct.
2. **Corresponding Angles:**
- Corresponding angles between \( JKLM \) and \( NPRS \) are as follows:
- \( \angle J \) and \( \angle S \) are both \( 60^\circ \).
- \( \angle K \) and \( \angle P \) are both \( 65^\circ \).
- \( \angle L \) and \( \angle R \) are both \( 140^\circ \).
- \( \angle M \) and \( \angle N \) are both \( 95^\circ \).
- Therefore,
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