Classifying Triangles
Angles in a Triangle
Triangle Congruence
Corresponding Parts
What's the Reason?
100
What kind of triangle has no congruent sides?
Scalene
100
All three angles in a triangle add up to what?
180 degrees
100
How many ways are there to prove two triangles are congruent?
BONUS QUESTION:
Name them all.
There are 5 ways to show congruence.
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)
Hypotenuse-Leg (HL)
100
Congruent angles are marked with what?
Congruent sides are marked with what?
Congruent angles are marked with arches (semi circles)
Congruent sides are marked with dash marks.
100
What is ALWAYS the first statement and reason in a two column proof?
Given
200
TRUE or FALSE:
If a triangle is acute, then only one of the angles is less than 90 degrees.
FALSE.
All of the angles are less than 90 degrees
200
In an equiangular triangle, all three angles will have what value?
60 degrees.
200
Hypotenuse Leg (HL) can only be used for what kind of triangle?
Right triangles
200
In the triangle congruence statement,
triangle ABC cong triangle XYZ
<A is congruent to which angle?
<X
200
In a proof, you just said two sides are congruent to each other. What should be your next step?
Mark the picture! Make the picture match the proof.
300
Classify the triangle by its SIDES and ANGLEs by the most specific names possible.
Scalene acute or acute scalene
300
Solve for x.
x = 23
300
Are the two triangles in the picture below congruent? If so, by what reason?
No, looks like AAS, but the pattern doesn't match!
300
TRUE or FALSE:
If two triangles are congruent, then all corresponding angles and all corresponding sides are congruent.
True.
This is called Congruent Parts of Congruent Triangles are Congruent, or CPCTC for short.
300
What is the reason the shared side would be congruent to itself?
Reflexive Property
It's just like looking in a mirror
400
Name all the ways to classify a triangle by its ANGLES, only the angles.
acute, obtuse, right, and equiangular
400
Solve for x.
x = 49
400
Based on the picture and triangle congruence statement, which side would be congruent to XV?
WH or HW
400
Given triangle ABC cong XYZ, and
AB = 5x + 2 and XY = 3x +10
Solve for x, then find the length of AB.
x = 4
AB = 22
400
What is the reason <AOB
cong
<COD?
Definition of Vertical Angles
'Bow tie' pictures mean to use vertical angles
500
Classify the following triangle
Hint: what does it mean to have two congruent angles?
Right Isosceles or Isosceles Right
If a triangle has two congruent angles, then the sides opposite those angles are congruent. Tricky!
500
In a triangle, one angle is two times the size of the smallest angle. The third angle is 20° more than the smallest angle.
Solve for x.
BONUS:
Find all the values of the angles.
x = 40
y = 80
z = 60
500
Are the two triangles congruent? If so, by what theorem?
No, AAA is not enough information to prove congruence.
500
Write a triangle congruence statement for the following two triangles?
triangle ABC cong triangle DEF
triangle ACB cong triangle DFE
triangle BAC cong triangle EDF
triangle BCA cong triangle EFD
triangle CAB cong triangle FDE
triangle CBA cong triangle FED
500
If B is the midpoint of XY, then what is true about the two segments. What would you write in a proof?
XB cong BY