Triangles: Angles and Sides |

**Triangles and Angles:**

The word **triangle** means 3 angles since "**tri**" is a prefix meaning 3 -- like in **tri**cycle.

A **triangle** is a **three sided closed figure** formed when

The 3 vertices create

The longest side is opposite or facing the largest angle just as the

smallest side is opposite or facing the smallest angle.

**Angle Definitions****:**

**A right angle** is exactly 90°. **A straight angle** is exactly 180°.

**an acute angle:** measures more than ( > ) 0° and less than ( < ) 90°.

**an obtuse angle:** measures more than ( > ) 90° but less than ( < ) 180°.

**complementary angles:** 2 acute angles that **sum to 90°** like 52° and 38°.

**suplementary angles:** 2 angles that **sum to 180°** like 152° and 28°.

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**Classification of Triangles:**

Triangles can be classified either by using their angles, their sides, or both. For instance, a triangle with a 90° angle, in which two sides are equal to each other is called an **isosceles right triangle**. The word **isosceles** tells us that **two sides are equal** and the word **right** tells us that there is a **right angle** in the triangle. Now, we define the different classifications of triangles.

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**1/ By Their Angles**

In an **acute triangle**, each of the 3 angles measures less than 90° but they always sum to 180°.

In a **right triangle**, there is **one 90° angle** and 2 **complementary** **acute angles** that sum to 90°.

The longest side is called the ** hypotenuse**. The other two sides are usually called legs.

In an **obtuse triangle**, there is **one obtuse** angle and **2 acute** angles.

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**2/ By Their Sides and Angles**

In a **scalene triangle**, there are no equal sides and no equal angles.

In an **isosceles **triangle, there are **2 equal sides **which create **2 equal angles**.

In an **equilateral **triangle, there are **3 equal sides **and** 3 equal angles**, of 60° each.

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Now get a pencil, an eraser and a note book, copy the questions,

do the practice exercise(s),then check your work with the solutions.

If you get stuck, review the examples in the lesson, then try again.

**Practice**

1) Label these triangles **acute, right, or obtuse**. Find the missing angle measure *x*.

(**reminder**:* the sum of the angles of a triangle is 180°*)

2) Label these triangles **scalene, isosceles, or equilateral**. Find the missing side measure *x*.

(**reminder**: *perimeter is the sum of the measures of the sides*)

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**Solutions**

1) Label these triangles **acute, right, or obtuse**. Find the missing angle measure *x*.

2) Label these triangles **scalene, isosceles, or equilateral**. Find the missing side measure *x*.

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