Side Lengths
Angles
Different Types
Solve for X
Bonus
100
Triangle ABC has side lengths 5 cm, 5 cm, and 3 cm. What type of triangle is this by side lengths?
Isosceles
100
What is the sum of the interior angles in any triangle?
180 degrees
100
What are the two main ways to classify triangles?
By sides and by angles
100
In triangle ABC, two angles measure 70° and 60°.
What is the value of x, the missing angle?
x = 50
(180 − 70 − 60)
100
Can a right triangle ever have an obtuse angle? Explain why or why not?
No! A right triangle has 90 degrees so the other two angles have to be complementary (less than 90 each).
200
Can a triangle with side lengths 4 cm, 6 cm, and 4 cm be scalene? Why or why not?
No. Two sides are the same length, so it is isosceles, not scalene.
200
In triangle ABC, angle A = 40° and angle B = 75°. What is the measure of angle C?
65 degrees
(180 − 40 − 75 = 65)
200
Match each triangle type to its description:
Isosceles
Right
Scalene
a) One angle is 90°
b) All sides are different
c) Two sides are equal
Isosceles → c
Right → a
Scalene → b
200
Angles J and K are supplementary.
Angle J = 3x−5
Angle K = 80°
Find the value of x.
3x−5+80=180
→ 3x=105
→ x=35
200
A triangle has angles measuring 45° and 75°.
Without solving, explain if this triangle could ever be a right triangle. Why or why not?
No. The third angle would be 60°, so none of the angles is 90°.
300
A triangle has three sides that each measure 9 cm. What kind of triangle is it?
Equilateral
300
Triangle XYZ has angles measuring 50°, 60°, and 70°.
What type of triangle is it based on its angles?
Acute triangle (all angles less than 90°)
300
Triangle ABC has angles measuring 90°, 45°, and 45°.
What is its classification by angles and sides?
Right and isosceles
300
Angles P and Q are complementary.
Angle P = 3x, angle Q = 2x+15
Find the value of x.
3x + 2x + 15 = 90
→ 5x = 75
→ x = 15
300
The angles of a triangle are in a ratio of 2:3:4.
What are the measures of each angle?
Let x be the unit: 2x+3x+4x=180
→ 9x=180
→ x=20
Angles: 40°, 60°, 80°
400
What do the lines mean in the triangles below?
The lines indicate which sides are equal in length.
400
Angle Q and angle R are supplementary.
If angle Q = 102°, what is the measure of angle R?
78 degrees
(180 − 102 = 78)
400
What type of triangle is this?
Scalene and obtuse
400
Triangle RST has angles:
∠R=2x+10
∠S=3x−10
∠T=40°
Find x.
(2x+10)+(3x−10)+40=180
→ 5x+40=180
→ x=28
400
A student says: “This triangle has angles 60°, 70°, and 60°, so it’s an equilateral triangle.”
Explain the mistake and classify the triangle correctly.
Incorrect: an equilateral triangle has three equal sides and three equal angles, each 60°.
This triangle has two equal angles, so it's isosceles, not equilateral.
500
Triangle DEF is isosceles and has a side that is 7 cm. Give one possible set of side lengths and explain why it fits.
Example: 7 cm, 7 cm, 5 cm.
It works because two sides are the same and one is different.
500
Two angles in a triangle are: x and 2x.
The third angle is 60°.
What is the value of x?
x=40
Explanation: x + 2x + 60 = 180
→ 3x+60=180
→ 3x=120
→ x=40
500
A triangle has two equal sides and no right angle.
It is not equilateral.
What are all the possible classifications?
Isosceles and either acute or obtuse
500
Triangle ABC is isosceles.
∠A = x+4
∠B = 2x+8
∠C is the same as ∠B
Find the value of x.
(x+4)+(2x+8)+(2x+8)=180
→5x+20=180
→ x=32
500
Create a triangle with three different angle measures that all add to 180°. None of the angles can be 90°, and one must be greater than 90°. List all three angles and justify the triangle’s type.
Example: 100°, 45°, 35°
Justification:
All angles are different → Scalene
One angle > 90° → Obtuse
Adds to 180° → ✅ Valid triangle