Download These triangles are congruent

Name:____________________________________
Chapter 4 Notes: 4.1
A
These triangles are congruent.
Color code the congruent corresponding ANGLES only.
Determine the congruent triangles:
(Be sure to use CONGRUENT symbol) __________
C
B
D
Determine the corresponding sides: (Be sure to use the
CORRESPONDING symbol)
These triangles are congruent.
E
W
R
T
Color code the congruent
corresponding SIDES only.
Determine the congruent triangles:
(Be sure to use CONGRUENT
symbol) ____________________
X
V
S
Determine the corresponding angles: (Be sure to use the CORRESPONDING symbol)
These triangles are congruent.
O
Color code the congruent corresponding SIDES.
Determine the congruent triangles:__________________
(Be sure to use CONGRUENT symbol)
L
P
Determine the corresponding sides and angles: (Be sure to
use the CORRESPONSING symbol)
R
4.2 Notes: Ways to Prove Triangles Congruent
SSS Postulate (Side-Side-Side)
If __________ _____________ of one triangle are congruent to __________ _________ of another triangle,
then the triangles are ____________________.
Example:
SAS Postulate (Side-Angle-Side)
If two sides and the ______________ ______________of one triangle are congruent to two sides and the
_____________ ________________ of another triangle, then the triangles are _______________________.
Example:
ASA Postulate (Angle-Side-Angle)
If two angles and the _______________ ___________ of one triangle are congruent to two angles and the
_______________ _______________ of another triangle, then the triangles are _____________________.
Example:
AAS Theorem (Angle-Angle-Side)
If you can show that _____________ ___________ and a __________ in one triangle are congruent to
____________ ____________and a _____________ in another triangle, then the triangles are congruent.
Example:
Shortcut due to ____________________
HL Theorem (Hypotenuse-Leg)
If the hypotenuse and leg of one _______________ triangle are congruent to the hypotenuse and leg of another
__________________ triangle, then the triangles are congruent. ONLY WORKS FOR __________ Triangles!
Example:
2 combinations DO NOT WORK!!!
___________ & __________
Shortcut due to ____________________
Note: SAA = AAS - Still one way!
Unit 4, Section 6-4 Notes
Theorem 6-2: If one side of a triangle is __________ than the second side, then the angle
___________ the first side is _________ than the angle opposite the second side
Angle_____ is larger than Angle _______
Theorem 6-3: If one angle of a triangle is __________than a second angle, then the side
___________ the first angle is longer than the side opposite the second angle
Draw Example:
Segment ______ is longer than segment ______
Corollary 1: The _______________ segment from a point to a line is the shortest segment
from a point to a line.
EXAMPLE:
Corollary 2: The perpendicular segment from a point to a plane is the shortest segment from
the point to the plane
Theorem 6-4: The SUM of the length of ______ ________ _________ of a triangle is
__________than the length of the third side
Example 1:
Example 2:
4.7 Notes: Median, Altitude, Perpendicular Bisector
MEDIAN: (always inside the triangle)
Definition:____________________________________________________________________________
Example:
ALTITUDE: (sometimes outside the triangle)
Definition:_____________________________________________________________________
Acute Triangle Example: The altitude is_______________ the triangle
Right Triangle Example: The altitude is a _________________ of a right triangle.
Obtuse Triangle Example: The altitude is ________________ the triangle
PERPENDICUALR BISECTOR:
R
Definition: _________________________________________
________________________________________________
T
S
X
ANGLE BISECTOR: _________________________________________________________
GEOMETRY/TRIGONOMETRY 2 EXTRA REVIEW
A Way to Prove Two Segments or Two Angles Congruent:
1) Identify two triangles in which the two segments or angles are corresponding parts.
2) Prove that the two triangles are congruent. (SSS, SAS, ASA…)
3) State that the two parts are congruent using the reason ___________.
Given: NR; M is the
midpoint of NR
1)
Statements
Reasons
KR  PN
Prove:
R
K
M
1
2
N
P
***First prove ______________
congruent
by __________. Then
use______________
2) Given: DF bisects EDG;
DE  DG
Statements
Reasons
Statements
Reasons
Prove: E  G
E
D
1
2
F
G
***First prove ______________
congruent
by __________. Then
use______________
3) Given: PR  SR;
PQ  SQ
Prove: P  S
Q
P
R
S