1. The document presents two geometry problems involving congruent triangles. 2. The first problem refers to Figure 1 and asks to show that AB = CB given that two angles are equal. It provides blank spaces to fill in the reasoning steps. 3. The second problem refers to Figure 2, shows an isosceles triangle ABC with BD as an angle bisector, and asks to show that AD = DC and that BD is perpendicular to AC. It also provides blank spaces.

1. Student’s Task1.1.66
Name: ............................ Date: ............................
Application of Congruence
1. Look at Figure 1.
B
A D C
Figure 1
Given ∠ABD = ∠CBD, show that AB = CB.
Fill in the following blank spaces:
Statement
a. ∠ BAD = ∠ BCD
b. ∠ ABD = ∠ CBD
c. ∠ BAD + ∠ ABD = ∠ BCD + ∠ ....
d. ∠ BAD+ ∠ ABD+ ∠ ADB =
∠ BCD+ ∠ CBD+ ∠ . .. = 1800
e. ∠ ADB = ∠ . . .
f. BD = BD
a. Given (in Figure 1)
b. .............
c. ..............
d. The sum of the
three angles in a
triangle is 180°.
e. clear
f. ...
14 / Student’s Worksheet – Similarity and Congruency

2. According to the requirement (. . . , . . . , . . . ), ΔABD ≅ Δ . . .
AB and ... are corresponding sides, so that AB = . . .
2. Look at Figure 2.
ΔABC is an isosceles triangle. B is the vertex of ΔABC.
∠ ABD = ∠ CBD. BD is the angle bisector of ∠B.
Show that:
a. AD = DC
b. BD is perpendicular to AC.
To solve the two problems above, fill in the following blank spaces.
B
A C
D
Figure 2
a) Look at ΔABD and ΔCBD.
1). AB = CB
2). ∠ ABD = ∠ . . .
3). BD = BD
4). According to the requirement ( . . . , . . . , . . . ), ΔABD ≅ Δ . . .
5). AD and ... are corresponding sides, so that AD = . . .
b) Based on the result in (a), it can be concluded that AD = ...
It means that BD is the segment bisector of ΔABC.
Since BD is the segment bisector of ΔABC, then BD . . . . . AC .
Mathematics for Junior High School Grade 9 / 15