Download Geometry 4-5 Proving Triangles Congruent

Geometry 4-5 Proving Triangles Congruent - ASA, AAS
Write a flow proof.
An included side
is the side of a polygon located
between two consecutive angles.
Given: ZX bisects WZY
Z
and YXW
Prove: WXZ~
= XZY
ZX bisects WZY
ZX bisects WXY
Given
~ YZX
WZX=
WXZ~
= YXZ
Def'n bisector
ZX ~
= ZX
Reflexive
WXZ ~
= XZY
ASA
Postulate 4.3 - Angle-Side-Angle (ASA) Congruence: If
two angles and the included side of one triangle are
congruent to two angles and the included side of a second
triangle, then the two triangles are congruent.
W
X
Y
R
S
Theorem 4.5 - Angle-Angle-Side (AAS) Theorem: If two
angles and the nonincluded side of one triangle are
congruent with two angles and the nonincluded side of a
second triangle, then the two triangles are congruent.
~ ST and RQ || ST
Given: RQ =
Prove: RUQ ~
= TUS
There are a few congruence theorems that apply ONLY to
right triangles.
Theorem 4.8 - Leg-Angle (LA) Congruence: If one leg and
an acute angle of one right triangle are congruent to one leg
and an acute angle of a second triangle, then the two
triangles are congruent. (Basically ASA)
Theorem 4.6 - Leg-Leg (LL) Congruence: If the legs of
one right triangle are congruent to the legs of a second right
triangle, then the triangles are congruent. (Basically SAS)
Theorem 4.7 - Hypotenuse-Angle (HA) Congruence: If
the hypotenuse and an acute angle of one right triangle are
congruent to the hypotenuse and an acute angle of a
second right triangle, then the two triangles are congruent.
(Basically AAS)
Statements
1. RQ || ST
2. RQU~
= UST
3. RUQ ~
= TUS
~ ST
4. RQ =
5. RUQ ~
= TUS
U
Reasons
1. Given
Q T
2. Alt Int 's Thm
3. Vert 's Thm
4. Given
5. AAS
Theorem 4.9 - Hypotenuse-Leg (HL) Congruence: If the
hypotenuse and a leg of one right triangle are congruent to
the hypotenuse and a leg of a second right triangle, then the
two triangles are congruent. (Basically SSS)