Download HOTS QUESTIONS STD: VII TRIANGLE AND ITS PROPERTIES

HOTS QUESTIONS
STD: VII
TRIANGLE AND ITS PROPERTIES
1. One of the angles of a triangle is 70° and the other two angles are equal.
Find these two angles.
2. The angles of a triangle are in the ratio 1:2:3.Determine the
corresponding angles.
3. The angles of a triangle are (x+21)° , x° and (2x-45)°.Find the value of x.
4. Of the three angles of a triangle ,one is three times the smallest and the
other is five times the smallest. Find the angles.
5. In a right triangle the two acute angles are in the ratio 7:11 .Find the acute
angles.
6. One angle of a triangle is 65°.Find the remainding two angles if their
difference is 20°.
7. The sum of two angles of a triangle is equal to its third angle. Determine
the measure of the third angle.
8. One of the exterior angle of a triangle is 80° and the interior opposite
angles are in the ratio 3:5.Find the angles of the triangle.
9. Compute the value of X
(a)
120°A
(b)
A
x
112
120
110°
X
B
C
B
C
(c)
D
B
E X
40
52°
A
C
10. Determine the angles of each of the following triangle.
(a)
(b)
2x
(x+10)
x
130
3x
150
(c )
36
2x 5x
11. In
ABC , AB=3cm ,BC = 4cm ,AC=5cm. Name the smallest and the largest
angles of the triangle .
12. A man goes 10m due east and then 24m due north .Find the distance from
the starting point.
13. ABC is an Isoceles right triangle , right –angled at C . Prove that AB^2 =
2AC^2.
14. Two poles of heights 6m and 11m stand on a plane ground. If the distance
between their feet is 12m.Find the distance between their tops
CONGRUENT TRIANGLE
15. Which of the following statements are true and which are false.
(a) All squares are congruent.
(b) If two squares have equal area, they are congruent.
(c) If two rectangles have equal area ,they are congruent.
(d) If two trianges are equal in area ,they are congruent.
16. In the following pairs of triangles , by applying sss condition , state which
are congruent .State the result in symbolic form.
D
5cm
C
A
3cm
6.7cm
3cm
9.2cm
3.1cm
9.2cm
A
5cm
B
3cm
B
C
3cm
D
17. By applying SAS congruence condition ,state which of the following pairs of
triangles are congruent .State the result in symbolic form.
(a)
A
D
(b)
A
O
B
C
B
C
18. State the condition by which the following pairs of triangles are congruent.
D
C
D
(a)
(b)
A
A
C
B
B
19. Which of the following pairs of triangles are congruent by ASA condition ?
(a)
A
(b)A
D
50
45
6.1cm 45
6.1cm
O
40
B
D
C
B
C
20. Draw a right triangle ABC .Use RHS condition to construct another triangle
congruent to it .
CONSTRUCTION OF TRIANGLES .
21. Draw an isosceles triangle in which each of the equal sides is of length 3 cm
and the angle between them is 45.
22. Draw ABC in which AB= 4.5cm ,BC=5cm ,CA=6cm .Also ,draw the
perpendicular bisector of BC.
23. Draw a right triangle having hypotenuse of length 5.4cm and one of the
acute angles of measure 60.
DATA HANDLING(Mean ,Median ,Mode)
24. Find the mean of
(a) the first seven natural numbers.
(b) the first five prime numbers .
© the first five multiples of 3.
(d) all the factors of 20.
25. The mean of six numbers 6,8,5,7,x and 4 is 7. Find the value of x.
26. The rainfall (in mm )recorded for a city on 15 days is as follows .
2.4,3.0,2.8,2.1,2.8,2.5,2.7,2.7,3.1,2.3,2.9,2.6,2.5,2.2,2.9.
(a) Rearrange the data in descending order.
(b) Determine the highest rainfall.
© Determine the lowest rainfall.
(d) Determine the range of the rainfall.
27. The median of the following observations ,arranged in ascending order is
22.Find x.
8,11,13,15,x+1,x+3,30,35,40,43.
28. The mean of 75 numbers is 35 .If each number is multiplied by 4 .Find the
new mean.
29. The scores in mathematics test (out of 25) of 15 students are as follows ,
19,25,23,20,9,20,15,10,5,16,25,20,24,12,20.
Find the mode and median of this data .Are they same?
DATA HANDLING
(DOUBLE BAR GRAPH)
30. Consider the following data gathered from a survey of colony :
Favourite
Cricket
Basket-ball Swimming Hockey
Athietics
Sport
Watching
1240
470
510
423
250
Participating 620
320
320
250
105
Draw a double bar graph choosing an appropriate scale.What do you infer from
the bar graph?
(a)Which sport is most popular ?
(b)What is more preferred watching or participating in sports?