NOTES AND QUESTIONS ON TRIANGLE (ATET)

Q: A triangle with one angle greater than 90 degrees

A. equilateral triangle 

B. Obtuse triangle 

C. acute triangle 

D. isosceles triangle 

Answer: B

Q: A triangle with all three angles less than 90 degrees 

A. equilateral triangle 

B. Obtuse triangle 

C. acute triangle 

D. isosceles triangle 

Answer: C

Q: A triangle having at least two equal sides

A. acute triangle 

B. isosceles triangle 

C. equilateral triangle 

D. obtuse triangle 

Answer: B

Q: A triangle with one angle equal to 90 degrees 

A. right triangle 

B. equilateral triangle 

C. acute triangle 

D. obtuse triangle 

Answer: A

Q: A triangle having three equal sides 

A. acute triangle 

B. obtuse triangle 

C. right triangle 

D. equilateral triangle 

Answer: D

Q: The sum of the measures of all three sides of a triangle 

A. area

B. perimeter 

C. Diameter 

D. radius 

Answer: B

Q: The sum of all the angles of a triangle 
A. 360 degrees 
B. 90 degrees 
C. 180 degrees 
D. 100 degrees 
Answer: C

Q: The perimeter of a  equilateral triangle is 15 cm. What is the length of a one side?
A. 3 cm
B. 45 cm
C. 15 cm
D. 5 cm
Answer: D

Q: In right triangle, the side opposite to right angle is called 
A. altitude 
B. hypotenuse 
C. angle bisector 
D. diagonal 
Answer: B

Classifying Triangles by Angles

There are two ways to classify triangles. To classify a triangle by angles means to categorize the triangle according to the types of angles that make up the triangle. To classify triangles by angles you must determine if each angle in the triangle is acute, right or obtuse. Once you have determined the types of angles you can classify the triangle as an Acute Triangle, Right Triangle, or Obtuse Triangle.

Let's review three different types of angles. 

         

                 

         

Now let's look at how that works with triangles.

Let's look at triangles with angle measures.

If all three angles are the same measure (60°) then the triangle is called EQUIANGULAR.

It will look like one of the two examples below.

                       

Let's review.

• If all the angles of the triangle are all less than 90° then the triangle is classified as an ACUTE TRIANGLE.

• If all the angles in the triangle are 60° or if they are all marked as congruent then the triangle is an ACUTE TRIANGLE but it is also a special triangle called an EQUIANGULAR triangle.

• If one of the angles is 90° then the triangle is a RIGHT TRIANGLE.

• If one of the angles is greater than 90° then the triangle is classified as an OBTUSE TRIANGLE.

Classifying Triangles by Sides

To classify a triangle by its sides means that we look at the side lengths of the triangle and make a determination as to whether it is an Equilateral, Isosceles and Scalene. To be an equilateral triangle all three side length must be exactly the same. An Isosceles triangle will have at least 2 side lengths that are the same. If all three sides of the triangle are different then the triangle is scalene.

1. If all the sides are equal (the same length) then the triangle is EQUILATERAL.

2. If 2 sides of the triangle are the same length then the triangles is an ISOSCELES triangle.

3. If all three sides of the triangle are a different length then the triangle is a SCALENE triangle.

Classifying a triangle is as simple as comparing the sides. If all three sides have the same length then it is an EQUILATERAL triangle, if only two sides have the same length then it is an ISOSCELES triangle and if there are no sides that have the same length then it is a SCALENE triangle. 

FINDING THE THIRD ANGLE

If you add all three interior angle measures together in a triangle it will always equal 180°.. To find a third angle you will subtract the sum of the two given angles from 180°. Look at the 3 examples below. 

72° + 50° + 58° = 180°

90° + 36° + 54° = 180°

Now let's look at what to do when we are given 2 angles but we are missing the 3rd angle.

Step 1: add the two angles that you are given together

Step 2: subtract your answer from 180.

Step 1: 125° + 20° = 145°

Step 2: 180° - 145° = 35°

x° = 35°

The key to finding the missing angle measure of a triangle is to remember that the sum of the interior angles of any triangle is always 180°. If you know 2 angles then you can subtract their sum from 180° to find the measure of the 3rdangle.