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--- **8.3 Similar Polygons** Solve the following: \[ \frac{2}{3} = \frac{6}{2y - 1} \] --- **E) Find the value of \( z \).** - \( z \) is in \( \angle V \). - Find the corresponding angle from \( ABCDE \sim RSTUV \). - Angles are congruent. Given: \[ m \angle V = m \angle E \] Equation: \[ 3z = 72 \] --- ### Example 3: \(ABCDE \sim RSTUV\) #### A) Write the scale factor. Look for 2 corresponding sides with numbers. According to \(ABCDE \sim RSTUV\), \(AB\) and \(RS\) both have numbers. I will use them to make the scale factor. It doesn’t matter which number is in the numerator. \[ \text{Scale factor} = \frac{RS}{AB} = \frac{4}{6} = \frac{2}{3} \] #### Diagrams Explanation - **Diagram on the left (RSTUV):** - Pentagon with vertices labeled \(R, S, T, U, V\). - Side \(RS\) is labeled with the length of 4. - Side \(VU\) is labeled with the length of 6. - Angle \(V\) is labeled \(3z^\circ\). - Side \(TU\) has a variable \(x\) without a defined length. - **Diagram on the right (ABCDE):** - Pentagon with vertices labeled \(A, B, C, D, E\). - Side \(AB\) is labeled with the length of 6. - Side \(BC\) is labeled with the length of 4.5. - Side \(CD\) is labeled \(2y - 1\). - Angle \(B\) is labeled \(140^\circ\). - Angle \(E\) is labeled \(72^\circ\). ### Additional Tasks #### B) Find the value of \(x\) #### C) Find the value of \(y\) (Note: Solutions for \(x\) and \(y\) involve further calculations using corresponding angles, sides, and the scale factor.)

--- **8.3 Similar Polygons** Solve the following: \[ \frac{2}{3} = \frac{6}{2y - 1} \] --- **E) Find the value of \( z \).** - \( z \) is in \( \angle V \). - Find the corresponding angle from \( ABCDE \sim RSTUV \). - Angles are congruent. Given: \[ m \angle V = m \angle E \] Equation: \[ 3z = 72 \] --- ### Example 3: \(ABCDE \sim RSTUV\) #### A) Write the scale factor. Look for 2 corresponding sides with numbers. According to \(ABCDE \sim RSTUV\), \(AB\) and \(RS\) both have numbers. I will use them to make the scale factor. It doesn’t matter which number is in the numerator. \[ \text{Scale factor} = \frac{RS}{AB} = \frac{4}{6} = \frac{2}{3} \] #### Diagrams Explanation - **Diagram on the left (RSTUV):** - Pentagon with vertices labeled \(R, S, T, U, V\). - Side \(RS\) is labeled with the length of 4. - Side \(VU\) is labeled with the length of 6. - Angle \(V\) is labeled \(3z^\circ\). - Side \(TU\) has a variable \(x\) without a defined length. - **Diagram on the right (ABCDE):** - Pentagon with vertices labeled \(A, B, C, D, E\). - Side \(AB\) is labeled with the length of 6. - Side \(BC\) is labeled with the length of 4.5. - Side \(CD\) is labeled \(2y - 1\). - Angle \(B\) is labeled \(140^\circ\). - Angle \(E\) is labeled \(72^\circ\). ### Additional Tasks #### B) Find the value of \(x\) #### C) Find the value of \(y\) (Note: Solutions for \(x\) and \(y\) involve further calculations using corresponding angles, sides, and the scale factor.)

Elementary Geometry For College Students, 7e
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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--- **8.3 Similar Polygons** Solve the following: \[ \frac{2}{3} = \frac{6}{2y - 1} \] --- **E) Find the value of \( z \).** - \( z \) is in \( \angle V \). - Find the corresponding angle from \( ABCDE \sim RSTUV \). - Angles are congruent. Given: \[ m \angle V = m \angle E \] Equation: \[ 3z = 72 \] ---
Transcribed Image Text:--- **8.3 Similar Polygons** Solve the following: \[ \frac{2}{3} = \frac{6}{2y - 1} \] --- **E) Find the value of \( z \).** - \( z \) is in \( \angle V \). - Find the corresponding angle from \( ABCDE \sim RSTUV \). - Angles are congruent. Given: \[ m \angle V = m \angle E \] Equation: \[ 3z = 72 \] ---
### Example 3: \(ABCDE \sim RSTUV\) #### A) Write the scale factor. Look for 2 corresponding sides with numbers. According to \(ABCDE \sim RSTUV\), \(AB\) and \(RS\) both have numbers. I will use them to make the scale factor. It doesn’t matter which number is in the numerator. \[ \text{Scale factor} = \frac{RS}{AB} = \frac{4}{6} = \frac{2}{3} \] #### Diagrams Explanation - **Diagram on the left (RSTUV):** - Pentagon with vertices labeled \(R, S, T, U, V\). - Side \(RS\) is labeled with the length of 4. - Side \(VU\) is labeled with the length of 6. - Angle \(V\) is labeled \(3z^\circ\). - Side \(TU\) has a variable \(x\) without a defined length. - **Diagram on the right (ABCDE):** - Pentagon with vertices labeled \(A, B, C, D, E\). - Side \(AB\) is labeled with the length of 6. - Side \(BC\) is labeled with the length of 4.5. - Side \(CD\) is labeled \(2y - 1\). - Angle \(B\) is labeled \(140^\circ\). - Angle \(E\) is labeled \(72^\circ\). ### Additional Tasks #### B) Find the value of \(x\) #### C) Find the value of \(y\) (Note: Solutions for \(x\) and \(y\) involve further calculations using corresponding angles, sides, and the scale factor.)
Transcribed Image Text:### Example 3: \(ABCDE \sim RSTUV\) #### A) Write the scale factor. Look for 2 corresponding sides with numbers. According to \(ABCDE \sim RSTUV\), \(AB\) and \(RS\) both have numbers. I will use them to make the scale factor. It doesn’t matter which number is in the numerator. \[ \text{Scale factor} = \frac{RS}{AB} = \frac{4}{6} = \frac{2}{3} \] #### Diagrams Explanation - **Diagram on the left (RSTUV):** - Pentagon with vertices labeled \(R, S, T, U, V\). - Side \(RS\) is labeled with the length of 4. - Side \(VU\) is labeled with the length of 6. - Angle \(V\) is labeled \(3z^\circ\). - Side \(TU\) has a variable \(x\) without a defined length. - **Diagram on the right (ABCDE):** - Pentagon with vertices labeled \(A, B, C, D, E\). - Side \(AB\) is labeled with the length of 6. - Side \(BC\) is labeled with the length of 4.5. - Side \(CD\) is labeled \(2y - 1\). - Angle \(B\) is labeled \(140^\circ\). - Angle \(E\) is labeled \(72^\circ\). ### Additional Tasks #### B) Find the value of \(x\) #### C) Find the value of \(y\) (Note: Solutions for \(x\) and \(y\) involve further calculations using corresponding angles, sides, and the scale factor.)
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