Download Exploring Congruent Triangles

LESSON 5: EXPLORING CONGRUENT TRIANGLES
Learning Outcomes: Learn to determine the minimum amount of information needed
to prove that two triangles are congruent.
If we are given the following triangle with measurements:
X
65˚
2.92m
1.95m
75˚
Y
40˚
2.74m
Z
If we wanted to duplicate this triangle, would we have to provide all the measurements?
Which three pieces of information could be provided for duplication to ensure that the
triangle is identical?
Which combinations of given side and angle measurements do not ensure that only one
size and shaped can be produced?
Which combinations of given side and angle measurements ensure that all the triangles
are congruent?
There are minimum sets of angle and side measurements that, if known, allow you to
conclude that two triangles are congruent.
If three pairs of corresponding sides are equal, then the triangles are congruent. This is
known as side-side-side congruence, or SSS.
A
B
X
C
Y
Z
If two pairs of corresponding sides and the contained angles are equal, then the
triangles are congruent. This is known as the side-angle-side congruence or SAS
A
B
X
C
Y
Z
If two pairs of corresponding angles and the contained sides are equal, then the
triangles are congruent. This is known as the angle-side-angle congruence or ASA
X
A
B
C
Y
Z
The symbol ∴ represents the word “therefore.” In geometry, this symbol is generally
used when stating a conclusion drawn from preceding facts or deductions.
Assignment: pg. 106 #1-4