1. ”TURGUT OZAL” COLLEGE
MATHEMATICS DEPARTMENT
Worksheet 3
NAME:
SURNAME:
CLASS: X
1. Complete the following definitions:
a. Two triangles are congruent if
____________________________
____________________________
____________________________
____________________________
b. Two triangles are similar if
____________________________
____________________________
____________________________
c. State Side – Angle – Side
congruency postulate:
____________________________
____________________________
____________________________
____________________________
d. State Angle – Side – Angle
congruency postulate:
____________________________
____________________________
____________________________
____________________________
e. State Side – Side – Side
congruency postulate:
____________________________
____________________________
____________________________
____________________________
2. ABC and DEF are parallel lines. BEG is a
straight line. Angle GEF = 47.
Work out the size of the angle marked x.
Give reasons for your answer.
3. ABCDE and EHJKL are regular pentagons.
AEL is an equilateral triangle. Work out
the size of angle DEH.
4.
The diagram shows part of a pattern made
from tiles. The pattern is made from two
types of tiles, tile A and tile B. Both tile A
and tile B are regular polygons. Work out
the number of sides tile A has.

2. ”TURGUT OZAL” COLLEGE
MATHEMATICS DEPARTMENT
Worksheet 3
NAME:
SURNAME:
CLASS: X
5. By using Euclidean theorem, find the
value of x, y, and z in the figure.
6. In the quadrilateral ABCD, AB is parallel DC
and m (∠DAB) = m(∠DBC).
a) Prove that triangles ABD and DBC are
similar.
b) If |AB|= 9cm and |DC| = 4 cm,
calculate the length of BD.
7. The radii of two spheres are in ratio 2 : 5.
The volume of the smaller sphere is 16
cm3
. Calculate the volume of the larger
sphere.
8.
9. In the given figure, AB is tangent to circle
with center O. measure of angle ADB is
52°. Find the measure of angle
a. CAB
b. CBA
c. DAC
10. It is given that NQ is 5 cm and QP is 4
cm. By using Euclidian theorem, find
the length of MQ, MP and MN in the
figure.
Given AB//CD |AB|=|CD|=8 cm,
|KD|=19 cm, |KC|=8 cm
|KB|=7b + 5 cm and |AK|=11 – a cm,
State the congruence and find a and b.
B
K
C
A
D

3. ”TURGUT OZAL” COLLEGE
MATHEMATICS DEPARTMENT
Worksheet 3
NAME:
SURNAME:
CLASS: X
11. Given that m(A) =m(KMC), |AC| = 8 cm,
|MC|=4 cm and the area of triangle MKC =
6cm2
. State the similarity and then find the
area of triangle ABC.
12. In the following figure, is given that
[GH]//[JI] and |GH| = |JI|. Prove that
triangle JGH is congruent to triangle JIH.
13. In the given figure, TB is tangent to circle
with center O. AB is diameter. If |TC| = 6
cm and |CA| = 10 cm, find |CB| = ?
14. In the given figure, AD is tangent to circle
with center O. measure of angle ADB is
56°. Find the measure of angle
a. CAD
b. ABD
c. BCA
15. In the following figures find the measure of
the missing angles.
a)
b)
c)
.
.
A
B C
K
M

4. ”TURGUT OZAL” COLLEGE
MATHEMATICS DEPARTMENT
Worksheet 3
NAME:
SURNAME:
CLASS: X
16. In the diagram, the lines PR and QS
intersect at point T. |PQ| = |RS| and [PQ]
// [RS]. Prove that triangles PQT and RST
are congruent.
17. Simplify
18. Make the letter in the square brackets the
subject of the formula

5. ”TURGUT OZAL” COLLEGE
MATHEMATICS DEPARTMENT
Worksheet 3
NAME:
SURNAME:
CLASS: X
19. Simplify as far as possible
𝑥2
+ 3𝑥 − 4
𝑥2 + 𝑥 − 12
÷
𝑥2
+ 4𝑥 − 5
𝑥2 + 4𝑥 − 21
2𝑥2
+ 𝑥 − 10
3𝑥2 − 2𝑥 − 8
×
3𝑥2
+ 10𝑥 + 8
𝑥2 + 6𝑥 + 8
=?
20. Write as a single fraction in its simplest
form.
21. Sketch the graph to identify the region A,
defined by
𝑥 > 0,
𝑥 + 𝑦 ≤ 7,
𝑦 > 𝑥
22. Sketch the graph to identify the region A,
defined by
𝑥 ≥ 0,
𝑥 + 𝑦 ≤ 5,
𝑦 > 𝑥
23. Sketch the graph to identify the region A,
defined by
𝑥 ≥ 0,
𝑥 + 2𝑦 ≤ 4,
𝑦 >
𝑥
2
24. Given that complete the
table:
25. Given that y varies as x2
and that y = 36
when x= 3. Find the value of y when x = 2.