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Geometry
Triangle Congruence
Notes 2.6B
Look for the
CLUES !!!!
F
B
Clues in the pictures for proving two triangles congruent.
1. TICK MARKS (p. 13) – Corresponding (matching) sides are congruent.
Therefore: AB  DF
D
A
2. TICK ARC MARKS (p. 13) – Corresponding (matching) angles are congruent.
Therefore: G  R
3. REFLEXIVE PROPERTY (p.106) - Shared side is congruent to itself.
Therefore: JH  JH
J
4. VERTICAL ANGLES (p. 30 & 120) - The nonadjacent angles formed when two lines cross.
Therefore: 1  2
5. BOX 900 ANGLE (p. 21) – All right angles are congruent.
Therefore: mW  90 0
R
G
H
2
1
B
W
6. PERPENDICULAR LINES (p.146) – Two lines that intersect at 900 angles.
Therefore: BAD  BAK
A
D
K
7. MIDPOINT (p.15) – A point that bisects or divides the segment into two congruent segments.
G is the mid point of FN
Therefore: FG  GN
F
G
N
8. ANGLE BISECTOR (p. 23) – A ray that divides an angle into two congruent angles. K
LR bisects KLH Therefore: KLR  HLR
R
L
H
9. THIRD ANGLE THEORM (p. 226) – If two angles of one triangle are congruent to two angles of
another triangle, then the third pair of angles are congruent.
10. PARALLEL LINES (p. 155 & 156) – If two lines are parallel and cut by a transversal, then
corresponding angles are congruent and alternate interior angles are congruent and alternate exterior angles
are congruent.
A
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
11. ISOSCELES TRIANGLE THEOREM (p. 273) - If two sides of a triangle are congruent,
then the base angles are congruent. Therefore: C  B
C
B
A
12. CONVERSE ISOSCELES TRIANGLE THEOREM (p.273) – If two angles of a triangle are
congruent, then the sides opposite those base angles are congruent. Therefore: AC  AB
C
B
13. EQUIANGULAR/EQUILATERAL THEOREM (p.274) – If a triangle is equilateral,
E
then it is equiangular. If a triangle is equiangular, then it is equilateral.
0
Then D  E  F and one angle is 60 . Then DE  EF  FD
D
F