Triangles
Triangle Proofs
Triangle Inequalities
Parts of Triangles
100
What are the three ways you can classify triangles based on their sides and how do you know which is which?
Equilateral - all 3 sides congruent
Isosceles - 2 sides congruent
Scalene - no sides congruent
100
There are two triangles, each with a right angle. The sides across from the right angles are congruent, and one of the other pairs of sides adjacent to the right angle are congruent.
What else do you need to state to use HL to prove these triangles are congruent?
That they are right triangles!!!!
100
Are you able to form a triangle with the side lengths 4, 13, 10? How do you know?
Yes, the two smallest sides when added are larger than the third side.
100
GH is a midsegment of triangle JLP. If JP is the side parallel to midsegment GH and is 24 units long, how long is midsegment GH?
12 units
200
Solve for x:
x = 23
200
What is the difference between the Isosceles Triangle Theorem and the Converse of the Isosceles Triangle Theorem?
Bonus +100: What is another name for the Isosceles Triangle Theorem?
Isosceles Triangle Thm: If two sides (legs) are congruent, then the two angles opposite those sides (base angles) are congruent.
Converse: If two angles (base angles) are congruent , then the two sides (legs) opposite those angles are congruent.
Bonus: Base Angle Theorem
200
What is the smallest side of the triangle if m angle A = 82° , m angle B = 33° , and m angle C = 65° ?
AC
200
Find the value of x when a triangle's midsegment is 7x and the side that runs parallel to it is 17x-18.
x = 6
300
Solve for x:
x = 9
300
Write a congruency statement for the triangles below:
NOT POSSIBLE!
The triangles are not necessarily congruent because SSA is not a thing ;)
300
In a right triangle ABC, m angle A=(2x+1)° and m angle B = (5x+5)°. Order the sides from least to greatest.
BC < AC < AB
300
Find the measure of each missing angle:
400
Find x, y, and z.
x = 64°
y = 52°
z = 77°
400
Can you prove any triangles congruent below?
If so, by what reason?
If so, write a valid congruence statement.
Yes, by SAS, triangleFEG \cong triangleGHF
400
What is a possible 3rd side to a triangle with side lengths 5 cm and 21 cm? How do you know?
Any value that satisfies the inequality 16 < x < 26 .
400
Describe an altitude of a triangle. What is the name of the intersection of all three altitudes?
Describe a median of a triangle. What is the name of the intersection of all three medians?
Altitude - Perpendicular line drawn from vertex to opposite side, orthocenter
Median - Line drawn from vertex to midpoint of opposite side, centroid
500
If triangle XYZ is equilateral and triangle WXY is isosceles, what is the measure of angle WXZ ?
m angle WXZ = 9°
500
Complete a two-column proof.
500
Which is longer, AC or DF? How do you know?
DF is longer than AC because of the Hinge Theorem ( m angle E > m angle B )
500
What is the inequality of the side lengths from least to greatest?
IJ < IG < GJ < GH < JH