Flashcards for Geometry Chapter 4
Front of the Card
Name five ways to prove triangles are congruent
Is there a donkey in geometry?
Is there a Side, Side, Angle in geometry?
CPCTC
If two angles are congruent on a triangle, then the
two sides opposite those two angles are also
congruent.
Name _____________________
Back of the Card
SSS (side, side, side)
SAS (side, angle, side)
ASA (angle, side, angle)
AAS (angle, angle side)
RHL (rt angles, hypotenuse, leg)
No, there is not an Angle, Side, Side theorem
No, SSA is a backwards donkey and there are no
donkeys in Geometry
Corresponding Parts of Congruent Triangles are
Congruent
Isosceles Triangle Theorem
“If angles, then sides”
If two sides are congruent on a triangle, then the
two angles opposite those two sides are also
congruent.
Isosceles Triangle Theorem
“If sides, then angles”
+ ABC ≅+ EFG, GE ≅ ____ by
+ ABC ≅+ EFG, GE ≅ CA by CPCTC
SSS
SAS
Not possible, there is no donkey (Angle Side Side)
+TSR ≅ ________ by _________
+TSR ≅+TVU by ASA
+STR ≅ ______ by __________
+STR ≅+UTR by AAS
Classify Triangles by Sides
Scalene Triangle: No congruent Sides
Isosceles Triangle: At least two congruent sides
Equilateral Triangle: All sides are congruent
Classify Triangles by Angles
Acute triangle: All three interior angles are acute
Obtuse triangle: One interior angle is obtuse
Right triangle: One interior angle is a right angle
*Equiangular: All angles measure 60
*Isosceles triangle: Two angles are congruent
The measure of an exterior angle on a triangle is equal
to the sum of the two remote interior angles.
m Angle 1 = 50 +65 = 115
Prove Segment BD is congruent to
Segment CA
Prove Angle T is congruent to Angle M
Statements
1. AB ≅ CD
Reasons
Given
2. (ABC ≅ (DCB
Given
3. BC ≅ BC
Reflexive Property
4. + ABC ≅+ DCB
Side Angle Side
5. BD ≅ CA
CPCTC
Statements
1. TA ≅ MA
Reasons
Given
2. MH ≅ TH
Given
3. HA ≅ HA
Reflexive Property
4. + AMH ≅+ ATH
Side Side Side
5. (T ≅ (M
CPCTC
Concepts from previous chapters to help you out:
Given: Diagram as shown
Vertical angles are congruent
U
F
N
1
T
2
M
What is true and why?
Given: N is the midpoint of FT
What is true and why?
U
F
(1 ≅ ( 2
N
1
FN ≅ NT
A midpoint divides a segment into two congruent
segments
T
2
M
JJJG
Given: AC bisects (BAD
What is true and why?
A
(1 ≅ ( 2
An angle bisector divides an angle into two
congruent angles.
1 2
B
C
D
Given: AC ⊥ BD
What else is true and why?
Then (ACB ≅ (ACD
Right angles are congruent
A
1 2
B
C
D
Given: SN & OW
What else is true and why?
N
O
5 6
8 7
S
(ACB and (ACD are right angles
Perpendicular lines form right angles
W
(5 ≅ ( 7
If two lines are parallel, then the alternate interior
angles are congruent.
Reflexive property: A segment is congruent to itself.
Why is NW ≅ WN ?
N
O
5 6
8 7
W
S
Given: SW & ON
What else is true and why?
N
( 6 ≅ (8
If two lines are parallel, then the alternate interior
angles are congruent.
O
5 6
8 7
W
S
Given: ΔABD is isosceles with vertex angle A.
What else is true and why?
A
1 2
B
C
D
AB ≅ AD
Legs of an isosceles triangle are congruent.