Triangle Congruence Theorems
Other Theorems
Congruence Statements
Finding measures
Triangle Properties
100
Which congruence theorem can be used to show
\triangle CAB \cong \triangle EDB ?
SSS Theorem
100
The Vertical Angles Congruence Theorem says that vertical angles are...
congruent.
100
Write a congruence statement for the following triangles
\triangle LMN \cong \triangle NQP
100
If two angles of a triangle measure 70º and 35º, what is the measure of the third angle?
75º
100
An equilateral triangle has ...
3 congruent sides
200
What triangle congruence theorem can be used to show
\triangle BAC \cong \triangle DEF ?
SAS Theorem
200
If two parallel lines are cut by a transversal, then the pairs of ______ angles are supplementary.
consecutive interior
OR
consecutive exterior
200
Which segment corresponds to \overline{BG} if ABGF \cong CDEF ?
Bonus: What is the value of x?
\overline{DE}
x=25
200
What is m \angle M ? If ML = 21 , what is LN ?
m\angle M = 60º , LN = 21
200
A triangle that has two congruent sides is called...
isosceles
300
Draw an example of two triangles that can be shown to be congruent by the AAS Theorem.
(Answers will vary)
300
Write the Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180º.
300
Write the segment congruence statement that you can get from the diagram using the reflexive property to help you show that \triangle PSQ \cong \triangle PTQ
\overline{PQ} \cong \overline{PQ}
300
What is m \angle 2 ?
139º
300
How many acute angles does an obtuse triangle have?
Two
400
What are the two side/angle combinations that CANNOT be used to show two triangles are congruent?
SSA and AAA
400
The Base Angles Theorem says: If two sides of a triangle are congruent, then ...
... the angles opposite them are congruent.
400
Identify all pairs of corresponding parts of these congruent quadrilaterals
Segments: \overline{QR} \cong \overline{WY} , \overline{RS} \cong \overline{XY} , \overline{ST} \cong \overline{YZ} , and \overline{TQ} \cong \overline{ZW}
Angles: \angle Q \cong \angle Q , \angle R \cong \angle X , \angle S \cong \angle Y , and \angle T \cong \angle Z
400
Find the vales of x and y.
x=30 and y=5
400
The hypotenuse of a triangle is...
the longest side on a right triangle
or
the side opposite the right angle on a right triangle
500
What three statements need to be made to use the HL Theorem?
1. The two triangles are right triangles
2. Their hypotenuses are congruent
3. One pair of legs is congruent
500
If two angles of one triangle are congruent to two angles of another triangle, then, ...
Bonus: What's the name of this theorem?
... the third angles are also congruent
Third Angles Theorem
500
If \angle XYZ \cong \angle ZXY , then which segments are congruent?
Bonus: What theorem did you use?
\overline{ZX} \cong \overline{ZY}
Base Angles Theorem (Converse)
500
Find the values of x and y.
x=85 , and
y=65
500
m\angle G = 20º , m\angle H = 40º , and
m\angle J = 120º .
List the sides of \triangle GHJ from longest to shortest.
\overline{GH}, \overline{GJ}, \overline{HJ}