Use the Pythagorean Theorem to find out if these are right triangles. Justify your answers. Yes or no for each ### Geometry: Triangle Sides Length#### Understanding Triangle DimensionsThe provided image shows a diagram of a triangle with three given side lengths. This example can help illustrate various geometric principles such as the properties of triangles and the application of the Pythagorean Theorem for right-angled triangles, though this specific triangle appears to be a general scalene triangle (a triangle with all sides of different lengths).#### Triangle c)- Left side length: 9.6 km- Right side length: 12.8 km- Base length: 16.0 kmThis representation can be used to discuss various topics in triangle geometry including the calculation of perimeter (sum of all side lengths) and exploring relationships between side lengths, or even diving into Heron's formula for finding the area of a triangle when all side lengths are known.This triangle can also serve in practical applications such as land surveying, navigation, or solving real-life problems where such measurements might be crucial. #### Practical Exercise- **Calculate the Perimeter:** The perimeter $ P $ of the triangle can be found by summing the lengths of all sides: \[ P = 9.6 \, \text{km} + 12.8 \, \text{km} + 16.0 \, \text{km} \] - **Discussion on Specific Properties:** Discuss how these side lengths would conform to the Triangle Inequality Theorem which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. Confirm this holds for the given side lengths of this triangle.By examining this triangular figure, students can gain practical insights into the properties and mathematical relationships inherent in triangular shapes.

By Pythagorean theorem( converse), If the square of the bigger side is equal to the sum of the…

Answered: Use the Pythagorean Theorem to find out…

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Use the Pythagorean Theorem to find out if these are right triangles. Justify your answers. Yes or no for each

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

Use the Pythagorean Theorem to find out if these are right triangles. Justify your answers. Yes or no for each

### Geometry: Triangle Sides Length

#### Understanding Triangle Dimensions

The provided image shows a diagram of a triangle with three given side lengths. This example can help illustrate various geometric principles such as the properties of triangles and the application of the Pythagorean Theorem for right-angled triangles, though this specific triangle appears to be a general scalene triangle (a triangle with all sides of different lengths).

#### Triangle c)

- Left side length: 9.6 km
- Right side length: 12.8 km
- Base length: 16.0 km

This representation can be used to discuss various topics in triangle geometry including the calculation of perimeter (sum of all side lengths) and exploring relationships between side lengths, or even diving into Heron's formula for finding the area of a triangle when all side lengths are known.

This triangle can also serve in practical applications such as land surveying, navigation, or solving real-life problems where such measurements might be crucial.

#### Practical Exercise

- **Calculate the Perimeter:**
The perimeter $ P $ of the triangle can be found by summing the lengths of all sides:
\[
P = 9.6 \, \text{km} + 12.8 \, \text{km} + 16.0 \, \text{km}
\]

- **Discussion on Specific Properties:**
Discuss how these side lengths would conform to the Triangle Inequality Theorem which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. Confirm this holds for the given side lengths of this triangle.

By examining this triangular figure, students can gain practical insights into the properties and mathematical relationships inherent in triangular shapes.

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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