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

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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,
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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