All triangles are similar, solve for x, y and z as appropriate. Round any decimal answers to the nearest 10th. In the image, two rectangles are displayed and labeled with their respective dimensions.1. **Smaller Rectangle**: - The height of this rectangle is 3 units. - The width is represented algebraically as $x + 1$.2. **Larger Rectangle**: - The height of this rectangle is 6 units. - The width of this rectangle is 8 units.Both rectangles are oriented horizontally with their longer sides on the bottom. The dimensions are clearly indicated in blue near the respective sides.This kind of diagram is typically used to solve problems involving the properties of rectangles, such as finding the area or perimeter, or applying the Pythagorean theorem in more complex scenarios combining algebra and geometry. The image depicts two quadrilaterals, labeled $ MNPQ $ and $ STUR $, with some sides and angles marked with measurements.### Quadrilateral $ MNPQ $:- This quadrilateral has four vertices labeled $ M $, $ N $, $ P $, and $ Q $.- Side lengths are given as: - $ PQ = 15 $ - $ MN = 18 $- The interior angle at vertex $ Z $ is marked as $ Z $.### Quadrilateral $ STUR $:- This quadrilateral has four vertices labeled $ S $, $ T $, $ U $, and $ R $.- Side lengths are given as: - $ ST = 25 $ - $ SR = 30 $- The interior angle at vertex $ U $ is marked as $ 115^{\circ} $.These quadrilaterals can be used to study various properties of quadrilateral shapes, such as side lengths, angles, and the relationship between these elements. Comparing the given side lengths and angles can be useful in solving geometric problems and understanding the characteristics of quadrilaterals in different contexts.

Answered: Image /qna-images/answer/0ecc8ec6-5fe4-4e53-899e-0be7db370ad8.jpg

Answered: 30 18 N M. R 115° 25 Q T y U ту 15 Р

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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All triangles are similar, solve for x, y and z as appropriate.

Round any decimal answers to the nearest 10th.

In the image, two rectangles are displayed and labeled with their respective dimensions.

1. **Smaller Rectangle**:
- The height of this rectangle is 3 units.
- The width is represented algebraically as $x + 1$.

2. **Larger Rectangle**:
- The height of this rectangle is 6 units.
- The width of this rectangle is 8 units.

Both rectangles are oriented horizontally with their longer sides on the bottom. The dimensions are clearly indicated in blue near the respective sides.

This kind of diagram is typically used to solve problems involving the properties of rectangles, such as finding the area or perimeter, or applying the Pythagorean theorem in more complex scenarios combining algebra and geometry.

The image depicts two quadrilaterals, labeled $ MNPQ $ and $ STUR $, with some sides and angles marked with measurements.

### Quadrilateral $ MNPQ $:
- This quadrilateral has four vertices labeled $ M $, $ N $, $ P $, and $ Q $.
- Side lengths are given as:
- $ PQ = 15 $
- $ MN = 18 $
- The interior angle at vertex $ Z $ is marked as $ Z $.

### Quadrilateral $ STUR $:
- This quadrilateral has four vertices labeled $ S $, $ T $, $ U $, and $ R $.
- Side lengths are given as:
- $ ST = 25 $
- $ SR = 30 $
- The interior angle at vertex $ U $ is marked as $ 115^{\circ} $.

These quadrilaterals can be used to study various properties of quadrilateral shapes, such as side lengths, angles, and the relationship between these elements. Comparing the given side lengths and angles can be useful in solving geometric problems and understanding the characteristics of quadrilaterals in different contexts.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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