Triangle Inequality
Triangle Properties
SSS, SAS, ASA Theorems
Name that Reason
Right Triangle
100
Is this a real triangle?
No
100
How do we know that <AEC=<DEB below?
What are vertical angles?
100
What is the theorem that can be used to prove each of the following pairs of triangles are congruent?
(Choose from SSS, SAS, ASA, AAS, or HL.)
SSS
100
What is the "Reason" for Statement #1 below?
What is "given"?
100
What is the equation for Pythagorean Theorem
a2+b2=c2
200
Can the lengths 3 cm, 4 cm, and 8 cm form a triangle?
Check all three conditions:
3 + 4 > 8 → 7 > 8 (False)
3 + 8 > 4 → 11 > 4 (True)
4 + 8 > 3 → 12 > 3 (True
✅ Answer: No, they do not form a triangle.
200
How do we know that CA=CA below?
Line segments are congruent to themselves. Reflexive Property.
200
What is the theorem that can be used to prove each of the following pairs of triangles are congruent?
(Choose from SSS, SAS, ASA, AAS, or HL.)
SAS
200
What is the reason for statement #3 below?
Line Segments are congruent to themselves. Reflexive Property
200
A right triangle has legs of 3 cm and 4 cm.
What is the length of the hypotenuse?
5
300
A triangle has sides 5 cm and 7 cm. What are the possible integer lengths for the third side (x)?
The third side must satisfy both:
✅ Answer:
2<x<12
300
Name an angle that point "E" is the vertex of?
1) <AEC (or <CEA)
2) <DEB (or <BED)
3) <AED (or <DEA)
4) <CEB (or <BEC>
NOTE:
300
What is the theorem that can be used to prove each of the following pairs of triangles are congruent?
(Choose from SSS, SAS, ASA, AAS, or HL.) 
ASA
300
What is the reason for statement #3 below?
What are vertical angles?
300
In a right triangle, the hypotenuse is 13 cm, and one leg is 5 cm.
Find the length of the other leg.
12
400
A builder has rods measuring 12 in and 20 in. What range of lengths can the third rod (x) be so it will form a triangle?
The third rod must be greater than 8 inches and less than 32 inches.
8<x<32
400
In the triangle below, if "D" is the midpoint of AC, what is AD congruent to?
What is DC?
400
What is the theorem that can be used to prove each of the following pairs of triangles are congruent?
(Choose from SSS, SAS, ASA, AAS, or HL.)
AAS
400
What is the reason for statement #2 below?
Given
400
A ladder leans against a wall. The foot of the ladder is 6 ft away from the wall, and the top of the ladder touches the wall 8 ft above the ground.
What is the length of the ladder?
10 ft
500
The sides of a triangle are x + 2, 3x, and 10.
Find all possible values of x.
✅ Answer:
2<x<6
500
IF DB bisects <B, what angle is <DBC congruent to?
<DBA or <ABD
500
What is the theorem that can be used to prove each of the following pairs of triangles are congruent?
(Choose from SSS, SAS, ASA, AAS, or HL.)
HL
500
1. Given
2. Given
3. Reflexive property
4. SSS
500
Find the distance between the points A(–2, 3) and B(4, 6) using the Pythagorean Theorem.
sqrt(45)= 3sqrt(5)