1. The document describes how to show that two triangles are congruent by cutting out one triangle and placing it on top of the other so that their corresponding sides and angles coincide. It states that for two triangles to be congruent, their corresponding sides must have equal lengths and corresponding angles must have equal measures. 2. It then gives another example of two triangles where the sides correspond to each other (are equal in length) and states that this is sufficient to show the triangles are congruent. 3. Finally, it instructs students to look at two additional pairs of triangles and identify their corresponding sides of equal length and corresponding angles of equal measure to determine if they are congruent.

1. Student’s Task11..55
Name: ............................ Date: ............................
Properties and Conditions
of Two Congruent Triangles
1. Look at the following figures.
ΔABC ≅ ΔPQR.
C R
A B P
Q
Figure 1
a. Copy ΔABC on a piece of cardboard.
b. Cut out the triangle, and then label the angles as shown in Figure 1.
c. Set the new ΔABC so that point A coincides with P, and point B
coincides with Q. Then fill in the following blank spaces:
(i). Point A coincides with point …, B with …, and C with …
(ii). Line segment AB coincides with PQ, so that AB = PQ
(iii). Line segment AC coincides with …, so that AC = …
(iv). Line segment BC coincides with …, so that BC = …
d. The sides that coincide with each other are called corresponding
sides.
AB and … are corresponding sides.
AC and … are corresponding sides.
BC and … are corresponding sides.
e. The angles that coincide with each other are called corresponding
angles.
Mathematics for Junior High School Grade 9 / 11

2. ∠CAB and ∠… are corresponding angles.
∠ABC and ∠… are corresponding angles.
∠ACB and ∠… are corresponding angles.
f. Your answers to e) and f) above show that
the length of the corresponding sides are ………. and
the size of the corresponding angles are ………..
2. In Figure 2 below, the sides of ΔABC correspond to those of ΔPQR, so
that AB = PQ, AC = PR and BC = QR.
P
A
R Q
Q
C B
Figure 2
a. Copy ΔABC on a cardboard.
b. Cut out the triangle on the cardboard, and label the angles as shown
in Figure 2.
c. Can you set the new ΔABC so that it coincides with ΔPQR?
d. What is your conclusion?
Therefore, if the three sides of ΔABC are the same as those of ΔPQR,
then ΔABC ≅ ΔPQR.
3. Look at the following pairs of congruent triangles. By measuring them,
find the corresponding sides of the same length and the corresponding
angles of the same size.
H
a. P Q
I
R J
12 / Student’s Worksheet – Similarity and Congruency

3. b.
K L
E
D
M F
4. Is ΔSTR ≅ ΔNMP? If so, determine the values of a, b and c.
S
N
67O
8
wO k
R
7
63O
T
8
aO
wO
M
b
k
cO
P

4. Mathematics for Junior High School Grade 9 / 13