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Use rhombus ABCD to answer the follwoing questions. AD= 10, AC=16, and mZABC = 130°

Use rhombus ABCD to answer the follwoing questions. AD= 10, AC=16, and mZABC = 130°

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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# Geometry: Rhombus ABCD Analysis **Topic: Geometry** **Course: Geometry 2** --- ### Use Rhombus ABCD to answer the following questions Given the following: - \( AD = 10 \) - \( AC = 16 \) - \( m \angle ABC = 130^\circ \) #### Diagram Description: A rhombus \(ABCD\) is depicted with diagonals \(AC\) and \(BD\) intersecting at point \(W\). The angles are as follows: - \(\angle ABC = 130^\circ\) The diagonals of the rhombus intersect at right angles (90 degrees) at \(W\), forming four right-angled triangles. ### Questions: 1. **AB =** - Answer: 10 2. **CW =** - Answer: 8 3. **The measure of angle \(BAD\) =** - Answer: [Fill in answer in degrees] 4. **The measure of angle \(CDB\) =** - Answer: [Fill in answer in degrees] 5. **The measure of angle \(DWA\) =** - Answer: [Fill in answer in degrees] 6. **The measure of angle \(WCD\) =** - Answer: [Fill in answer in degrees] ### Explanation: When working with the given angles and properties of the rhombus, apply the following geometrical properties: - **Properties of a rhombus**: All sides are equal, and the diagonals bisect each other at right angles. - Diagonals of a rhombus split it into four right triangles. ### Steps to Solve the Missing Angles: 1. **Angle \(BAD\)**: - Since \(\angle ABC\) is 130 degrees and diagonals bisect each other, \(\angle BCD = 130^\circ\). - \( \angle BAD = 180^\circ - 130^\circ = 50^\circ\). 2. **Angle \(CDB\)**: - Since rhombus diagonals form 90 degrees at the intersection, - \( \angle CDA = 90^\circ\). 3. **Angle \(DWA\)**: - Since point \(W\) is the intersection of diagonals, forming right angles, - \( \angle DWA = 90^\
Transcribed Image Text:# Geometry: Rhombus ABCD Analysis **Topic: Geometry** **Course: Geometry 2** --- ### Use Rhombus ABCD to answer the following questions Given the following: - \( AD = 10 \) - \( AC = 16 \) - \( m \angle ABC = 130^\circ \) #### Diagram Description: A rhombus \(ABCD\) is depicted with diagonals \(AC\) and \(BD\) intersecting at point \(W\). The angles are as follows: - \(\angle ABC = 130^\circ\) The diagonals of the rhombus intersect at right angles (90 degrees) at \(W\), forming four right-angled triangles. ### Questions: 1. **AB =** - Answer: 10 2. **CW =** - Answer: 8 3. **The measure of angle \(BAD\) =** - Answer: [Fill in answer in degrees] 4. **The measure of angle \(CDB\) =** - Answer: [Fill in answer in degrees] 5. **The measure of angle \(DWA\) =** - Answer: [Fill in answer in degrees] 6. **The measure of angle \(WCD\) =** - Answer: [Fill in answer in degrees] ### Explanation: When working with the given angles and properties of the rhombus, apply the following geometrical properties: - **Properties of a rhombus**: All sides are equal, and the diagonals bisect each other at right angles. - Diagonals of a rhombus split it into four right triangles. ### Steps to Solve the Missing Angles: 1. **Angle \(BAD\)**: - Since \(\angle ABC\) is 130 degrees and diagonals bisect each other, \(\angle BCD = 130^\circ\). - \( \angle BAD = 180^\circ - 130^\circ = 50^\circ\). 2. **Angle \(CDB\)**: - Since rhombus diagonals form 90 degrees at the intersection, - \( \angle CDA = 90^\circ\). 3. **Angle \(DWA\)**: - Since point \(W\) is the intersection of diagonals, forming right angles, - \( \angle DWA = 90^\
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