Identify the similar triangles in the diagram, then sketch them so the corresponding sides and angles have the same orientation. ### Directions: Identify the similar triangles in each case. Recall that similar triangles have the same shape, meaning corresponding sides and angles have the same properties.#### Problem 1Consider the triangle $LZM$ and $LJK$. In the diagram, two right triangles are shown:- Triangle $ LZK $ has a right angle at $ M $.- Triangle $ JMK $ has a right angle at $ K $.**Diagram Explanation:**In the diagram, we have two overlapping triangles sharing the same height from point $ L $ to point $ K $. The point $ M $ forms a right angle with both points $ J $ and $ K $.**Question:** Identify the pairs of similar triangles in the image above.#### Problem 2Consider the triangle $XY$ and the triangle $XZ$. Both triangles share the same base $X$, but form different angles:- Triangle $ XYZ $ has a right angle.- Smaller triangle inside the larger triangle also has a right angle at point $X$ and is marked.**Diagram Explanation:**In the diagram, two right triangles are shown, one overlapping the other:- One is the larger triangle $ XYZ $.- The other is a smaller, internal triangle sharing the same perpendicular height from $Y$ to $ Y$.**Question:** Identify the pairs of similar triangles in the image above.### Directions: Solve for $ x $.#### Problem 3A set of similar triangles is given, with various sides marked as $x$, representing scales and dimensions to be calculated based on given similar properties. (Note: The details of Problem 3 are not visible in the provided image)

Answered: Image /qna-images/answer/9c03fec8-3898-4213-a02f-77df6a26ed55.jpg

Answered: Identify the similar triangles in the…

Identify the similar triangles in the diagram, then sketch them so the corresponding sides and angles have the same orientation.

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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Question

Identify the similar triangles in the diagram, then sketch them so the corresponding sides and angles have the same orientation.

### Directions: Identify the similar triangles in each case. Recall that similar triangles have the same shape, meaning corresponding sides and angles have the same properties.

#### Problem 1
Consider the triangle $LZM$ and $LJK$. In the diagram, two right triangles are shown:

- Triangle $ LZK $ has a right angle at $ M $.
- Triangle $ JMK $ has a right angle at $ K $.

**Diagram Explanation:**

In the diagram, we have two overlapping triangles sharing the same height from point $ L $ to point $ K $. The point $ M $ forms a right angle with both points $ J $ and $ K $.

**Question:** Identify the pairs of similar triangles in the image above.

#### Problem 2
Consider the triangle $XY$ and the triangle $XZ$. Both triangles share the same base $X$, but form different angles:

- Triangle $ XYZ $ has a right angle.
- Smaller triangle inside the larger triangle also has a right angle at point $X$ and is marked.

**Diagram Explanation:**

In the diagram, two right triangles are shown, one overlapping the other:

- One is the larger triangle $ XYZ $.
- The other is a smaller, internal triangle sharing the same perpendicular height from $Y$ to $ Y$.

**Question:** Identify the pairs of similar triangles in the image above.

### Directions: Solve for $ x $.

#### Problem 3
A set of similar triangles is given, with various sides marked as $x$, representing scales and dimensions to be calculated based on given similar properties. (Note: The details of Problem 3 are not visible in the provided image)

Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.

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