Types of Triangles
This type of triangle has all three sides of equal length and all three angles equal to 60∘. What is it?
Equilateral triangle
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be __________ than the length of the third side.
Greater
The sum of the interior angles of any triangle is always ________?
180 degrees
The sum of the exterior angles of any triangle is always ________?
360 degrees
Two triangles have the same shape but different sizes. What type of triangles are they?
Similar Triangles
This type of triangle is known for having angles that are all less than 90∘, and its sides are of different lengths. What is it?
Acute Scalene triangle
Can a triangle be formed with side lengths of 3 cm, 4 cm, and 8 cm? Use the Triangle Inequality Theorem to explain your answer.
NO
(Explanation: 3+4=7 is not greater than 8, so a triangle cannot be formed.)
In a triangle, one angle measures 40∘ and another measures 90∘. What is the measure of the third angle?
50 degrees
What theorem tells us the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles?
Exterior Angle Theorem
Two triangles have all corresponding sides equal. What type of triangles are they?
Congruent Triangles
In a triangle, one angle measures 120∘ and the other two angles are equal. Classify the triangle by both its angles and its sides and what is the other two angle's degree measure.
Obtuse Isosceles triangle
30
Can a triangle be formed with side lengths of 16 cm, 4 cm, and 12 cm? Use the Triangle Inequality Theorem to explain your answer.
NO
(Explanation: 4+12=16 is not greater than 16, so a triangle cannot be formed.)
A triangle has two equal angles of 70∘. What is the measure of the third angle?
40 Degrees
If one exterior angle of a triangle is 120∘, what is the measure of its adjacent interior angle?
60 degrees
In two similar triangles, the sides of one triangle are 3, 4, and 5 units long, while the longest side of the second triangle is 15 units. What is the length of the shortest side of the second triangle?
9 Units
A triangle has interior angles measuring 40∘ and 70∘, and its longest side measures 12 cm. Classify the triangle by its angles and sides
Acute Isosceles Triangle
Given a triangle with side lengths a=8 cm, b=6 cm, and c=x cm, which of the following could x not be: 2, 7, 8, or 13?
2 and 13
In an isosceles triangle, the vertex angle measures 30∘. What is the measure of each base angle?
75∘
A triangle has an exterior angle measuring 110∘. If one of the opposite interior angles is 50∘, what is the measure of the other interior angle?
60 degrees
You are given two triangles where two angles of one triangle measure 40∘ and 70∘, and two angles of the other triangle measure 40∘ and 70∘. What can you conclude about these triangles? Give the reason from the conditions of a similar/ congruent triangle
They are similar because they have 2 congruent angles so AA
A triangle has two angles that measure 45∘ and one side that is 10 cm long. Classify the triangle by both its angles and its sides.
Isosceles Right triangle
If two sides of a triangle are 7 cm and 10 cm, what are the possible lengths of the third side, according to the Triangle Inequality Theorem?
Between 3 cm and 17 cm
In a triangle, one interior angle is four times the smallest angle, and the third angle is 30∘ greater than the smallest angle. What are the measures of all three angles?
25, 55, 100
One exterior angle of a triangle measures 15+x∘. If one of the opposite interior angles is 7+x∘, and the remaining interior angle is 4x. What is x?
x = 2
In two similar triangles, the ratio of corresponding sides is 2:3. If the sides of the first triangle is 6 ,8 ,10.
What is the perimeter of the second triangle
So it would have a perimeter of 36
Lucas is trying to create a map scale of a house for his neighborhood. He is going to make the top of the house a triangle. The sides of the top of the house on his map measure 6 cm, 8 cm, and 10 cm. The perimeter of the top of the house is 72 ft. What are the lengths of the sides of the house if the two triangles are similar?
18 ft, 24 ft, 30 ft