Interior Triangles Sum

Triangle Sum Theorem

By Emily Smith

Multiple Choice

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. 

• 45°
• 90°
• 180°
• 360°

The triangle may be acute, obtuse, right, isosceles, scalene, equilateral, or equiangular. All of the angles STILL sum to 180 degrees. ​

The sum of the interior angles of ANY triangle will ALWAYS be 180 degrees. ​

55^o + 90^o + x^o = 180^o

​145^o + x^o = 180^o

​x^o = 180^o - 145^o

x^o = 35^o

​​<1 + <2 + <3 = 180^o

​x^o + 120^o + 28^o = 180^o

​x^o + 148^o = 180^o

​x^o = 180^o - 148^o

x^o = 32^o

<C + <A + <B = 180^o

​

Multiple Choice

Find the measure of the missing angle.

• 30^o
• 110^o
• 150^o
• 40^o

Multiple Choice

Find x.

• 75 degrees

• 45 degrees

• 63 degrees

• 85 degrees

Multiple Choice

Find the measure of the missing angle.

• 90^o
• 10⁰
• 130^o
• 50^o

Multiple Choice

Find the measure of the angle indicated. 

• 139°
• 66°
• 138°
• 116°

Multiple Choice

Find the measure of each angle indicated.

• 50
• 20
• 29
• 48

Multiple Choice

Find the measure of each angle indicated.

• 50
• 55
• 60
• 70

Multiple Choice

A student is trying to construct triangles using four different sets of angles. The angles in each set are given below. Which set will form a triangle?

• 45°, 65°, 70°

• 150°, 110°, 100°

• 50°, 50°, 50°

• 90°, 90°, 90°

All three of these interior angles measure LESS than 90 degrees. That makes this an acute triangle.

​Acute Triangle

​

​An obtuse triangle has ONE (1) interior angle that is LARGER than 90 degrees and TWO (2) acute angles.

​​Obtuse Triangle

​

A right triangle has ONE (1) interior angle that measures EXACTLY 90 degrees and TWO (2) acute angles.

Right Triangle

​

An equiangular triangle has THREE (3) congruent angles. In an equiangular triangle, all angles will always measure 60 degrees.

Equiangular Tri.

​

No triangle can have MORE THAN ONE (>1) obtuse angle. EVER. Forever.

A triangle with NO congruent sides. The hash marks represent that each side length is different and the angle arcs represent that all of the angle measures are different.

Scalene Triangle

​A triangle with TWO (2) congruent side lengths and TWO (2) congruent angles. The hash marks represent the congruent sides and the angle arcs represent the congruent angles.

Isosceles Triangle

A triangle with THREE (3) congruent sides. The hash marks represent the congruent sides and the angle arcs represent the congruent angles.

Equilateral Triangle

​

This is an acute isosceles triangle​.

1. <O and <B are congruent angles

2. OA & BA are ​congruent side lengths

​

<A + <O + <B = 180^o

Acute Triangle

​

This is an acute equilateral and equiangular triangle.

1. All three sides are congruent.

2. All three angles are congruent.

3. All three angles measure

   less than 90^o.​

​

​

<1 + <2 + <3 = 180^o

Acute Triangle

​This is an obtuse scalene triangle.

1. One (1) angle is obtuse.

2. Each side is a different length.

​

​

<1 + <2 + <3 = 180^o

Obtuse Triangle

This is an obtuse isosceles triangle.

1. Two (2) sides are congruent.

2. One (1) angle is obtuse and two (2) angles are acute. ​

​

​

<1 + <2 + <3 = 180^o

Obtuse Triangle

This is an isosceles right triangle.

1. There is one (1) right angle and there are two (2) acute angles.

2. There are two (2) congruent sides. ​

​

45^o + 45^o + 90^o = 180^o

Right Triangle

This is a scalene right triangle.

1. There is one (1) right angle and there are two (2) acute angles.

2. There are no congruent sides. ​

​

<1 + <2 + <3 = 180^o

Right Triangle

Poll

Can a right triangle be equilateral?

• Yes!

• NO

NO. A right triangle

cannot be equilateral.

An equilateral triangle is ALSO equiangular.

• In a right triangle, all three (3) angles will NEVER be congruent.

• There can only be ONE (1) ​right angle in any triangle, so AT MOST, two (2) angles in a right triangle can be congruent.

• A right triangle will always have a longest and shortest side, because of the 90^o angle.

Multiple Choice

Classify each triangle by its angles and sides.

• Acute, Isosceles

• Obtuse, Isosceles

• Right, Scalene

• Equiangular, Equilateral,

• Acute, Scalene

Multiple Choice

Classify each triangle by its angles and sides.

• Acute, Isosceles

• Obtuse, Isosceles

• Right, Scalene

• Equiangular, Equilateral,

• Acute, Scalene

Multiple Choice

Classify each triangle by its angles and sides.

• Acute, Isosceles

• Obtuse, Isosceles

• Right, Scalene

• Equiangular, Equilateral,

• Acute, Scalene

Multiple Choice

Which of the following is false?

• A triangle can be drawn with 3 acute angles.

• A triangle can be drawn with 2 obtuse and one acute angles.

• A triangle can be drawn with only one obtuse angle and two acute angles.

• A triangle can be drawn with only one right angle and two acute angles.

Multiple Choice

What type of triangle has only one obtuse angle and two congruent sides?

• Right Isosceles Triangle
• Obtuse Isosceles Triangle
• Right Scalene Triangle
• Acute Scalene Triangle

Multiple Choice

What type of triangle has only acute angles and no congruent sides?

• Right Isosceles Triangle
• Obtuse Isosceles Triangle
• Right Scalene Triangle
• Acute Scalene Triangle