---### Right Triangle Proportions#### Problem Statement:Given right triangle $ \triangle ABC $ with a right angle at $ C $ and $ m∠C = 61^\circ $, right triangle $ \triangle RST $ with a right angle at $ T $ and $ m∠R = 29^\circ $, which proportion in relation to $ \triangle ABC $ and $ \triangle RST $ is not correct?#### Diagram:The problem includes a diagram showing two right-angled triangles, $ \triangle ABC $ and $ \triangle RST $, each with their right angles and respective angles labeled.#### Proportions to Consider:1. $ \frac{AB}{RS} = \frac{KI}{AC} $2. $ \frac{BC}{ST} = \frac{AB}{RS} $3. $ \frac{AC}{ST} = \frac{RS}{EF} $4. $ \frac{AB}{AC} = \frac{RS}{EF} $#### Multiple-Choice Options:- $ \circ $ A- $ \circ $ B- $ \circ $ C- $ \circ $ D#### Important Notes:- Analyze each proportion to determine which one is not correct based on the properties of similar triangles.- Right triangles with common angles have proportional corresponding sides.### Explanation of Diagram:- The first diagram shows $ \triangle ABC $ with angles labeled, including the right angle at $ C $.- The second diagram shows $ \triangle RST $ with its angles labeled, including the right angle at $ T $.### Task:Identify and explain which proportion among the given options is not correct.---This transcription is designed to facilitate understanding and problem-solving for students studying geometry, specifically the properties of similar triangles and right triangles.

Answered: Image /qna-images/answer/3d3ccc41-eaff-4038-a710-e4936169d921.jpg

Given right triangle ABC with a right angle at Cand m261", right triangle RST with right angle at Tand m/R = 29°. which proportion in relation to triangle ABC and triangle RST is not correct? O BC RS O BC AC %3D RT A 坦 B. C.

Given right triangle ABC with a right angle at Cand m261", right triangle RST with right angle at Tand m/R = 29°. which proportion in relation to triangle ABC and triangle RST is not correct? O BC RS O BC AC %3D RT A 坦 B. C.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

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### Right Triangle Proportions

#### Problem Statement:
Given right triangle $ \triangle ABC $ with a right angle at $ C $ and $ m∠C = 61^\circ $, right triangle $ \triangle RST $ with a right angle at $ T $ and $ m∠R = 29^\circ $, which proportion in relation to $ \triangle ABC $ and $ \triangle RST $ is not correct?

#### Diagram:
The problem includes a diagram showing two right-angled triangles, $ \triangle ABC $ and $ \triangle RST $, each with their right angles and respective angles labeled.

#### Proportions to Consider:
1. $ \frac{AB}{RS} = \frac{KI}{AC} $
2. $ \frac{BC}{ST} = \frac{AB}{RS} $
3. $ \frac{AC}{ST} = \frac{RS}{EF} $
4. $ \frac{AB}{AC} = \frac{RS}{EF} $

#### Multiple-Choice Options:
- $ \circ $ A
- $ \circ $ B
- $ \circ $ C
- $ \circ $ D

#### Important Notes:
- Analyze each proportion to determine which one is not correct based on the properties of similar triangles.
- Right triangles with common angles have proportional corresponding sides.

### Explanation of Diagram:
- The first diagram shows $ \triangle ABC $ with angles labeled, including the right angle at $ C $.
- The second diagram shows $ \triangle RST $ with its angles labeled, including the right angle at $ T $.

### Task:
Identify and explain which proportion among the given options is not correct.

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This transcription is designed to facilitate understanding and problem-solving for students studying geometry, specifically the properties of similar triangles and right triangles.

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