Triangles Test

Result

Triangles Test - 21

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Weekly Quiz Competition

Question 1
1 / -0

If the lengths of the sides of a triangle does not satisfy the rule of $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$, then that triangle does not contain a

A
Alternative angle

B
Equal angle

C
Acute triangle

D
Right angle

Solution

If if any triangle
$$a^{2}+b^2=c^2$$ is not satisfied then the triangle is not a right angled triangle.
Option $$D$$ is correct.
Question 2
1 / -0

Similarity is represented by :

A
$$\sim$$

B
$$=$$

C
$$\simeq $$

D
none of these

Solution

$$\sim$$ is used to represent similarity.
So, answer is option $$A.$$
Question 3
1 / -0

Which one of the four trapezoids is not similar to the other three?

A
A

B
B

C
C

D
D

Solution

Two shapes are similar if the only difference is size (and possibly the need to turn or flip one around).
Trapezoid B is similar to Trapezoid A because it has the same shape but has been rotated.
Trapezoid C is similar to Trapezoid A because it has the same shape but a different size.
Only Trapezoid D has a different shape to the other three.
Question 4
1 / -0

In a right angle triangle $$ ABC$$ with sides $$a, b, c;$$
If pythagoras theorem states that $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$ then which of the following is true:

A
$$\displaystyle c=\sqrt { { a }^{ 2 }+{ b }^{ 2 } } $$

B
$$\displaystyle c=\sqrt { { a }^{ 2 } } -{ b }^{ 2 }$$

C
$$\displaystyle c=\sqrt { { a }^{ 2 } } \times { b }^{ 2 }$$

D
$$\displaystyle c=\sqrt { { a }^{ 2 } } \div { b }^{ 2 }$$

Solution

If $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$, then is $$\displaystyle c=\sqrt { { a }^{ 2 }+{ b }^{ 2 } } $$
Therefore, A is the correct answer.
Question 5
1 / -0

Any triangle with sides a, b, c, if $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$,then the angle between a and b measures.

A
$$\displaystyle { 180 }^{ o }$$

B
$$\displaystyle { 100 }^{ o }$$

C
$$\displaystyle { 170 }^{ o }$$

D
$$\displaystyle { 90 }^{ o }$$

Solution

If $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$, c is the hypotenuse and angle opposite to the hypotenuse is a right angle in Pythagoras theorem which lies between a and b and measure of right angle is $$\displaystyle { 90 }^{ o }$$.
Therefore, D is the correct answer.
Question 6
1 / -0

Two triangles are $$ABC$$ and $$PQR$$ are similar, then symbolically it is represented as:

A
$$ABC \sim PQR$$

B
$$ABC \simeq PQR$$

C
$$ABC = PQR$$

D
none of these

Solution

Two similar triangles can be represented as $$ABC∼PQR.$$
Question 7
1 / -0

In any right angle triangle, the hypotenuse is .......... than any one of the other sides, but less than their sum.

A
Smaller

B
Shorter

C
Greater

D
None of the above

Solution

In any right triangle, the hypotenuse is greater than any one of the other sides, but less than their sum because to form a triangle sum of any two sides must be greater than the third side.
Question 8
1 / -0

All congruent figures are similar but the similar figures are not congruent. Is this statement true or false?

A
False

B
Both A and C

C
True

D
Not applicable

Solution

Congruent figures are of same shape and size. So they are similar but similar figures are not congruent as they might not be of the same size.
Therefore, C is the correct answer.
Question 9
1 / -0

In $$\displaystyle \Delta HKI,\overline { HJ } $$ is a perpendicular bisector of $$\displaystyle\overline { KI } $$. By which criterion will you prove $$\displaystyle \Delta HJK\sim \Delta HJI$$.

A
SAS similarity criterion

B
AAA similarity criterion

C
AA similarity criterion

D
SSS similarity criterion

Solution

In $$\displaystyle \Delta HJK$$ and $$\displaystyle \Delta HJI$$
$$\displaystyle\overline { HJ } =\overline { HJ } $$ (given $$\displaystyle\overline { HJ } $$ is a perpendicular bisector of $$\displaystyle\overline { KI } $$)
$$\displaystyle \angle HJK$$ and $$\displaystyle \angle HJI$$ (definition of perpendicular lines)
$$\displaystyle \angle HJK= \angle HJI$$ (right angles)
$$\displaystyle\overline { KJ } =\overline { JI } $$ (J is midpoint)
$$\displaystyle \Delta HJK\sim \Delta HJI$$ (SAS similarity criterion)
Therefore, A is the correct answer.
Question 10
1 / -0

A Pythagorean Triplet always...............of all even numbers, or two odd numbers and an even number.

A
Consists

B
Does not consists

C
Ambiguous

D
Integers

Solution

A Pythagorean Triple always consists of all even numbers, or two odd numbers and an even number.
Therefore, A is the correct answer.

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Re-Attempt Weekly Quiz Competition

Triangles Test - 21

Result

Triangles Test - 21

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SHARING IS CARING

Question 1

Alternative angle

Equal angle

Acute triangle

Right angle

Solution

Question 2

$$\sim$$

$$=$$

$$\simeq $$

none of these

Solution

Question 3

A

B

C

D

Solution

Question 4

$$\displaystyle c=\sqrt { { a }^{ 2 }+{ b }^{ 2 } } $$

$$\displaystyle c=\sqrt { { a }^{ 2 } } -{ b }^{ 2 }$$

$$\displaystyle c=\sqrt { { a }^{ 2 } } \times { b }^{ 2 }$$

$$\displaystyle c=\sqrt { { a }^{ 2 } } \div { b }^{ 2 }$$

Solution

Question 5

$$\displaystyle { 180 }^{ o }$$

$$\displaystyle { 100 }^{ o }$$

$$\displaystyle { 170 }^{ o }$$

$$\displaystyle { 90 }^{ o }$$

Solution

Question 6

$$ABC \sim PQR$$

$$ABC \simeq PQR$$

$$ABC = PQR$$

none of these

Solution

Question 7

Smaller

Shorter

Greater

None of the above

Solution

Question 8

False

Both A and C

True

Not applicable

Solution

Question 9

SAS similarity criterion

AAA similarity criterion

AA similarity criterion

SSS similarity criterion

Solution

Question 10

Consists

Does not consists

Ambiguous

Integers

Solution

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