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The Mathematics Department
Stage: 2nd Prep
1st term
Revision "Geometry"
Unit One: Medians of a Triangles
& the Isosceles triangle
[1] Choose the correct answer:
1] In the isosceles triangle the number of axes of symmetry is ……….
a) one
b) two
c) three
d) zero
2] If the measure of two angles in a triangle are 70° and 40°, then the triangle is
………..
a) equilateral
b) isosceles
c) scalene
d) right-angled
3] The bisector of the vertex angle in the isosceles triangle ………….
a) only cuts the base
b) bisects the base & is perpendicular to it
c) bisects the base only
d) is perpendicular to the base only
4] In the equilateral triangle the number of axes of symmetry is ……….
a) one
b) two
c) three
d) zero
5] In the isosceles triangle if the measure of one of its base angles is 50°, then the
measure of the vertex angle equals ……….°
a) 50
b) 70
c) 65
d) 80
6] In ∆ ABC: If m B = 45°, m C = 90°, then the number of axes of symmetry is
……….
a) 1
b) 2
c) 3
d) zero
7] In ∆ ABC: if m B = 90°, m A = 60°, then AC = ……….
a) BC
b) AB
c) ½ AB
d) 2 AB
8] AD is a median in the right-angled triangle ABC at A, M is the intersection point of
the medians. If BC = 12 cm, then AM = ……. cm
a) 6
b) 3
c) 4
d) 8
9] The point of intersection of the medians of a triangle divides each of them in ratio
…….. from the vertex.
a) 1 : 2
b) 2 : 1
c) 3 : 1
d) 3 : 2
10] If ABC is a triangle in which: AB = AC and m A = 60°, then the number of axes
of symmetry in it is ………….
a) 1
b) 2
c) 3
d) zero
11] The axis of symmetry of a line segment is the straight line …………
a) perpendicular to it
b) that bisects it
c) that is parallel to it
d) perpendicular to it from its midpoint
12] The measure of the exterior angle of the equilateral triangle = …….°
a) 180
b) 60
c) 120
d) 90
1
13] The length of the hypotenuse of the right-angled triangle equals …….. the length
of the median from the vertex of the right angle.
1
1
1
a)
b)
c)
d) 2
2
4
3
14] The length of the side opposite to the angle of measure 30° in the right-angled
triangle equals …….. the length of the hypotenuse.
1
1
1
a)
b)
c)
d) 2
2
4
3
15] The number of medians in the triangle equals ………..
a) 1
b) 2
c) 3
d) zero
[2] Complete the following:
1] In ∆ ABC, if m A = 70°, m B = 30°, then the greatest side of the triangle is
…………..…
2] If M is the point of intersection of the medians in ∆ ABC, AD is a median whose
length is 9 cm, then AM = ……….… cm.
3] In the right-angled triangle, the length of the hypotenuse equals ………….… the
length of the side opposite to the angle whose measure is 30°.
4] The two base angles in the isosceles triangle are …………………………….
5] The straight line that is perpendicular to a line segment from its midpoint is called
…………………………...
6] In ∆ ABC, if m (  A) = m (  B) = 60°, then the number of symmetry axes to this
triangle = ……………….
7] If ∆ XYZ has only one symmetry axis and m XYZ = 120°, then m X = …………°
8] The point that is equidistant from the two terminals of a line segment belongs to
…………………………...
9] The point of intersection of the medians of the triangle divides each of them with
the ratio ………... : ……….. from the vertex
10] In ∆ ABC, if D is the midpoint of BC , then AD is called ……………..…
11] The number of medians in the right-angled triangle is ……………..
12] The line segment drawn between the two midpoints of two sides in a triangle is
…………………………….. and its length equals …………………………….
13] XY // ZL and XY = ZL, then the quadrilateral XYZL is called ……………………………
2
14] The length of the side opposite the angle whose measure is 30° in the rightangled triangle = …………………………………………….
15] The medians of the triangle intersect at ……………………………
16] In ∆ ABC right-angled triangle at B, if D is the mid-point of AC and AC = 8 cm
then BD = …………………..
17] In ∆ ABC, if D is the mid-point of AC and BD = ½ AC, then m B = ………………
[3] Using data given for each the following figures, find the required below each
figure:
A
A
//
10 cm
D
5 cm
//
B■
C
B
AC = …………….. cm
D
9 cm
14 cm
D
//
30°
//
//
M
×
E
B■
C
AC = ………. cm
BD = ………. cm
MD = ………. BD & MD = ………. cm
A
F
E
D
E
●
\\
●
\\
●
\\
●
M
■
B
D
If AB = 8cm, BC =10cm & AC = 9cm
DE = …..…. cm
DF = …..…. cm
FE = …..…. cm
Perimeter of ∆ DEF = …..…. cm
C
C
B
If BC = 12 cm, BE = 9 cm & MC = 8 cm
DE = …..…. cm
ME = ………. cm
MD = ………. cm
[4] In the following figures, name the equal sides:
A
70°
2x-5
A
2y
C
50°
C
BD = …….. cm
AB = ………….. cm
The perimeter of ∆ ABD = …..… cm
A
\\
C
A
//
×
30°
AB = …………….. cm
A
B■
■
■
3y+5°
C
B
3
x+25°
B
[5] In the opposite figure:
∆ ABC in which AB = AC, BX = CY
, m (C) = 50° and m (BAX) = 30°
i) Prove that: ∆ XYA is isosceles triangle
ii) Find m (AYC)
A
30°
\\
C
50° /
Y
[6] In the opposite figure:
ABC is an isosceles triangle in which
AB = AC, BD bisects ABC, CD bisects  ACB.
Prove that: ∆ DBC is isosceles.
C
//
\
X
B
A
\\
//
D


●
●
B
A
[7] In the opposite figure:
AB = BC, AD = 20 cm.
BD  AC .
1) Find the length of AC
2) Prove that: ∆BCD is isosceles
20cm
\
D
B
[8] In the opposite figure:
∆ ABC in which AB = BC, BC bisects ABC and cuts
AC at D. Draw DE // CB and DE ∩ AB = {E}.
Prove that: BE = ED
\
C
A
D
C
4
■
>
>
E
●
●
B