Triangles Test

Result

Triangles Test - 45

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Weekly Quiz Competition

Question 1
1 / -0

In figure 8, $$m\angle R > m\angle T$$ and $$\overline{RP}$$ and $$\overline{TP}$$ are bisectors of $$\angle R$$ and $$\angle T$$ respectively. Then

A
$$PT < RP$$

B
$$PT = RP$$

C
$$RP + PT > RS + ST$$

D
$$PT > RP$$

E
no relationship between PT and RP can be determined from the given information
Question 2
1 / -0

In $$\triangle PQR$$, if the measure of $$\angle Q$$ is $$50^o$$ and the measure of $$\angle P$$ is $$p^o$$, and if $$\overline{PQ}$$ is longer than $$\overline{PR}$$, then

A
0 < p < 40

B
0 < p < 80

C
40 < p < 80

D
80 < p < 90

E
80 < p < 130

Solution

$$PQ>PR$$ (given)
$$\Rightarrow \angle R>50^o$$ -----------(1)
Also, $$\angle P+\angle Q+\angle R=180^o$$
$$\Rightarrow P+50^o+\angle R=180^o$$
$$\Rightarrow \angle R=130-p >50$$ (using 1)
$$\Rightarrow 130-p>50$$
$$\Rightarrow p<80$$
$$\therefore 0<p<80$$
Question 3
1 / -0

In fig 3, if AB $$=$$ AC and AP $$=$$ AQ, then by which congruence criterion $$\Delta PBC \cong \Delta QCB$$

A
SSS

B
ASA

C
SAS

D
RHS
Question 4
1 / -0

The equation of circumcircle of an

equilateral triangle is $$ x^2 + y^2 + 2gx + 2fy + c = 0$$ and one vertex

of the triangle is $$(1, 1)$$. The equation of incircle of the triangle is

A
$$4(x^2+y^2)=g^2+f^2$$

B
$$4(x^2+y^2) +8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f)$$

C
$$4(x^2+y^2) +8gx+8fy=g^2+f^2$$

D
None of these
Question 5
1 / -0

If $$a, b, c$$ are sides of a triangle, then

A
$$\sqrt a + \sqrt b > \sqrt c $$

B
$$\left| {\sqrt a - \sqrt b } \right| > \sqrt c $$

C
$$\sqrt a + \sqrt b < \sqrt c $$

D
None of these

Solution

Given: Sides of the triangle $$a, b$$ and $$c$$.

Triangle inequality theorem: According to this theorem,
[The sum if lengths of any two sides of triangle is greater than the length of its third side.]

i.e. $$a + b > c$$
$$b + c > a$$
$$a + c > b$$

For example, $$a = 3cm, b = 4 cm, c = 5 cm$$ then
$$3 + 4 > 5 ; \, 7 > 5$$
$$4 + 5 > 3 ; \, 9 > 5$$
$$3 + 5 > 4 ; \, 6 > 4$$

$$\sqrt{a} + \sqrt{b} > \sqrt{c}$$
$$\sqrt{3} + \sqrt{4} > \sqrt{5}$$
$$1.73 + 2 > 2.24$$
$$3.73 > 2.24$$

It means the correct option is $$(A)$$. i.e.
$$\sqrt{a} + \sqrt{b} > \sqrt{c}$$
Question 6
1 / -0

In a $$\triangle PQR,$$ if $$\angle R>\angle P,$$ then which of the following cannot be true ?

A
$$QR>PQ>PR$$

B
$$PR>PQ>QR$$

C
$$PQ>PR>QR$$

D
$$PQ>QR>PR$$

Solution
Question 7
1 / -0

Two sides of a triangle are 7 cm and 25 cm, then the number of all possible integral values of third side of the triangle is

A
11

B
14

C
12

D
13

Solution
Question 8
1 / -0

In $$\Delta ABC,BC$$ is the greatest side. Then,

A
$$\angle A$$ must be greater that $${60^o}$$

B
$$\angle A$$ must be greater than $${75^0}$$ but less than $${90^0}$$

C
$$\angle A$$ must be greater than $${45^0}$$ but not necessarily greater than $${60^0}$$

D
none of these
Question 9
1 / -0

Take any pointy $$O$$ in the interior of a triangle $$PQR$$. Is

A
$$OP+OQ>PQ?$$

B
$$OQ+OR>QR?$$

C
$$OR+OP>RP?$$

D
All of the above.

Solution
Question 10
1 / -0

If the sides of triangle are 4 cm and 6 cm then the third side cannot be ... cm.

A
8

B
10

C
5

D
8.5

Solution