Use the Pythagorean Theorem to find out if these are right triangles. Justify your answer Yes or no for each ### Geometry: Understanding Triangles#### Triangular Measurements (Diagram a)The following diagram represents a triangle with the lengths of its sides clearly marked:- Side 1: 3 cm- Side 2: 4 cm- Side 3: 5 cm**Explanation:**This is a simple diagram of a triangle where each side is labeled with its respective length. This particular triangle is a right-angled triangle, as it follows the Pythagorean theorem ($a^2 + b^2 = c^2$), where $a$, $b$, and $c$ are the lengths of the sides. For this triangle:\[ 3^2 + 4^2 = 9 + 16 = 25 = 5^2 \]Hence, the side opposite the right angle is 5 cm (the hypotenuse).Understanding such diagrams is fundamental in geometry, as it helps in recognizing and solving problems related to triangular shapes and their properties.### Key Concepts:- **Right-Angled Triangle:** A triangle with one angle measuring 90 degrees. The side opposite this angle is the longest side, known as the hypotenuse.- **Pythagorean Theorem:** In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.This diagram and the accompanying explanation serve as a basic illustration and application of elementary geometric principles.

The formula for the Pythagoras theorem helps to validate the given statement. The formula for the…

Answered: a) 3 сm 4 cm 5 сm

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

### Geometry: Understanding Triangles

#### Triangular Measurements (Diagram a)

The following diagram represents a triangle with the lengths of its sides clearly marked:

- Side 1: 3 cm
- Side 2: 4 cm
- Side 3: 5 cm

**Explanation:**
This is a simple diagram of a triangle where each side is labeled with its respective length. This particular triangle is a right-angled triangle, as it follows the Pythagorean theorem ($a^2 + b^2 = c^2$), where $a$, $b$, and $c$ are the lengths of the sides. For this triangle:
\[ 3^2 + 4^2 = 9 + 16 = 25 = 5^2 \]
Hence, the side opposite the right angle is 5 cm (the hypotenuse).

Understanding such diagrams is fundamental in geometry, as it helps in recognizing and solving problems related to triangular shapes and their properties.

### Key Concepts:
- **Right-Angled Triangle:** A triangle with one angle measuring 90 degrees. The side opposite this angle is the longest side, known as the hypotenuse.
- **Pythagorean Theorem:** In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

This diagram and the accompanying explanation serve as a basic illustration and application of elementary geometric principles.

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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