1) In the isosceles triangle ABC, BA=BC. M and N are points on [AC] such that
[MA] is congruent to [MB] and [NB] is congruent to [NC]. Show that triangles
AMB and CNB are congruent.
2) ABCD is a square. C' is a point on BA and B' is a point on AD such that BB'
and CC' are perpendicular.
̂ 𝐵 ; BC = BA and 𝐶𝐵̂𝐶′ = 𝐵𝐴̂𝐵′ = 90
Given: 𝐵 ̂
𝐶 ′ 𝐶 = 𝐴𝐵′
Show that B'B= C'C are congruent.
3) SEC is any triangle. “O” is the symmetry of “E” with respect S; “L” is the
symmetric of “C” with respect to “S”.
a) Represent the figure.
b) Prove that the two triangles ESC and LSO are congruent.
̂ cuts
4) ABC is an isosceles triangle of vertex A the bisector of angle 𝐴𝐵𝐶
[BC] at “M”
a) Let “N” be a point on [AM]; Prove that the two triangles ANB and
ANC are congruent.
5) KLM is an isosceles triangle where KL = LM = 5cm. The perpendicular
drown from K to [LM] cuts [LM] at R.
a) Represent the above figure.
b) Prove that the two triangles KLR and KMR are congruent
(Use the HL theory)
6) Write the following in the form of one power.
a) (43)2 × 40 =
b) 36 × 915 =
3 8
3 19
4
4
c) ( ) × ( )
d)
e)
f)
g)
h)
i)
=
(52)3 =
(3 × 3)5 =
52 × 518 =
105 × 1000 =
1,000,000,000 =
107 × 100 =
j) (1018 × 1015 )0 =
k) 105 × 104 =
l) 1 =
7) Write in the form of product of two powers
a)
b)
c)
d)
e)
f)
g)
(7.3)3 × 610 × (7.3)17 × 6 =
49 × 52 × 410 × 517 =
(22 )2 × 2 × (83 )3 × 86 =
9 × 16 × (3 × 4)2 =
25 × 30 =
(8.5)2 × 610 × (8.53 )2 × 60
(56 × 72 × 8)0 × 80 × 10
8) Perform the following equations.
a) (−4) × (−3) =
b) (+9) × (−5) =
c) 1800 × 3 – 5 × 33 =
d) ( 10 – 2 × 5 )5 − 7 × 22 × (5 – 3 )2 × 0 =
e) 9 ×9 +(2× 4)2 =
f) 6 × 106 + 80 × 105 + 3 × 102 =
g) 32 × 5 – 5 × 23 =
h) 104 – 62 =
i) −42 =
j) (−2)3 =
k) (−25) ÷ (5 ) =
l) ( 25) ÷ ( −5) =
m) −6 × 6 − (2 + 6) =
n) (8 − 7 × 2) + (−5 − 1) − (−5) =
o) (0) ÷ 12 =
p) 3.5 − 4.2 × [ ( 6 − 8 × 3 ) + 11.2] =
q) (−8 ) + ( −5 )=
r) (+9 ) − (+17)=
s) (−3.1 ) − (−5.5) + (−3.2) =
t) (+9.4 ) + (−4.6 ) =
u) (+5) + (−9) + (+10) + (−4) + (+16.2) =
v) (+4) − (−10) + (+1) + (−9) + (+15) + (−8) =
w) (−9) + (−9) + (2.3) + (−4) + (+1.2) =
6) Complete the following table.
A
-6
3
10
3
B
-2
-9
-10
100
a+b
a–b
opp (b)
7) Write the Prime Factorization of each of the following numbers.
a) 35
b) 60
c) 15
d) 36
e) 17
f) 130
g) 78
𝑎3