--- **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
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
Related questions
Question
Example E
![---
**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:
\[
3z = 72
\]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88296449-4020-45ce-a35f-28e4157e48b0%2Fb9befc5e-5072-495c-96dd-3ac518d93059%2Fh3tmaap.jpeg&w=3840&q=75)
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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88296449-4020-45ce-a35f-28e4157e48b0%2Fb9befc5e-5072-495c-96dd-3ac518d93059%2Ffhjpckd_processed.jpeg&w=3840&q=75)
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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