Is it acute Obtuse or right triangle? Justify the answer in numbers please. ## Determining the Nature of Triangle $ \triangle ABC $### Problem Statement:Determine if $ \triangle ABC $ is acute, obtuse, or right.The coordinates of the points are:- $ A(1, 5) $- $ B(-3, -3) $- $ C(1, -5) $### Options:1. $ \bigcirc $ Acute triangle2. $ \bigcirc $ Obtuse triangle3. $ \bigcirc $ Right triangle (Selected)4. $ \bigcirc $ This triangle is impossible### Question:Justify your answer with an equation or inequality:\[ \text{Input Field:} \ [\textit{justify in numbers}] \ \] [This field allows you to enter your mathematical justification.]### Graphical Representation:On the right side of the page, there is a graph with a coordinate system ranging from $-8$ to $8$ on both axes. The points are marked and color-coded as follows:- Point $ A(1, 5) $ is marked with a red dot.- Point $ B(-3, -3) $ is marked with a green dot.- Point $ C(1, -5) $ is marked with a blue dot.### Hint:*Move points around to help you.* This indicates that you can interact with the points on the graph to further understand their positions and the type of triangle they form.### Instructions:To determine the type of triangle $ \triangle ABC $:1. Calculate the lengths of the sides using the distance formula.2. Use the Pythagorean theorem to check if the triangle is right-angled.3. Justify your conclusion with appropriate calculations and equations.### Explanation:To verify if $ \triangle ABC $ is a right triangle, calculate the distances between each pair of points to find the lengths of the sides. Then, use the Pythagorean theorem to check if the sum of the squares of the two shorter sides equals the square of the longest side.

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Answered: Determine if AABC is acute, obtuse, or…

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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Is it acute Obtuse or right triangle? Justify the answer in numbers please.

## Determining the Nature of Triangle $ \triangle ABC $

### Problem Statement:
Determine if $ \triangle ABC $ is acute, obtuse, or right.

The coordinates of the points are:
- $ A(1, 5) $
- $ B(-3, -3) $
- $ C(1, -5) $

### Options:
1. $ \bigcirc $ Acute triangle
2. $ \bigcirc $ Obtuse triangle
3. $ \bigcirc $ Right triangle (Selected)
4. $ \bigcirc $ This triangle is impossible

### Question:
Justify your answer with an equation or inequality:

\[ \text{Input Field:} \ [\textit{justify in numbers}] \ \] [This field allows you to enter your mathematical justification.]

### Graphical Representation:
On the right side of the page, there is a graph with a coordinate system ranging from $-8$ to $8$ on both axes. The points are marked and color-coded as follows:
- Point $ A(1, 5) $ is marked with a red dot.
- Point $ B(-3, -3) $ is marked with a green dot.
- Point $ C(1, -5) $ is marked with a blue dot.

### Hint:
*Move points around to help you.* This indicates that you can interact with the points on the graph to further understand their positions and the type of triangle they form.

### Instructions:
To determine the type of triangle $ \triangle ABC $:
1. Calculate the lengths of the sides using the distance formula.
2. Use the Pythagorean theorem to check if the triangle is right-angled.
3. Justify your conclusion with appropriate calculations and equations.

### Explanation:
To verify if $ \triangle ABC $ is a right triangle, calculate the distances between each pair of points to find the lengths of the sides. Then, use the Pythagorean theorem to check if the sum of the squares of the two shorter sides equals the square of the longest side.

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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Determine if AABC is acute, obtuse, or right. A(1,5), B(-3,-3), C(1,-5) Acute triangle Obtuse triangle Right triangle This triangle is impossible