Construction of a Right Triangle Whose One Side and Hypotenuse Are Given

Q. Which vertex of $\Delta$ABC is right angled if $\overline{AB}$ = 8 cm, $\overline{AC}$ = 6 cm, and $\overline{BC}$ = 10 cm?

1. $\angle C$
2. $\angle A$
3. $\angle B$
4. $AorC$

Q.

You are given the measurement of two sides of a right angled triangle such that these sides enclose the right angle. What else do you need in order to draw a triangle?

1. Length of the third side

2. Measure of one angle

3. Do not need anything else as the triangle can be constructed from the given data

4. Either length of one side or measure of one angle

Q.

Pavan followed the steps given below to construct a triangle

Right-angled triangle LMN, with hypotenuse $LN=8cm$ and side $MN=5cm$.

Step 1: Draw line 'l'.
Step 2: Mark a point on 'l' and name it M.
Step 3: Draw a line segment $MN=5cm$ on 'l' .
Step 4: Construct a right angle $\angle$ XMN at M.
Step 5: Draw an arc with N as the centre and radius equal to $8cm$, such that it intersects MX.
Step 6: Mark the point of intersection as L.
Step 7: Join points L and N.

Are the steps followed by him correct?

If it is correct then enter "Yes” if no then enter "No”.

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Q. Steps for the construction of a right triangle LMN in which $\angle M={90}^{\circ }$, MN = 4 cm and LN = 6.2 cm is given below. Choose the correct order.

1. Draw a line segment XY.
2. Construct a line segment MP, sufficiently large such that $\angle NMP={90}^{\circ }$
3. With N as centre and radius 6.2 cm draw an arc, cutting MP at L, join NL.
4. Locate M and N on XY such that MN = 4 cm.

1. 1, 4, 2, 3
2. 2, 1, 3, 4
3. 2, 3, 1, 4
4. 1, 4, 3, 2

Q. A right triangle DEF is constructed with DE = 5 cm, $\angle F={90}^{\circ }$ and DF = 4 cm. Choose the correct statement from the following.

1. DF is the hypotenuse of $\Delta$ DEF
2. EF = 3 cm
3. $\angle E+\angle D={180}^{\circ }$
4. $\angle E={90}^{\circ }$

Q. Construct a right-angled isosceles triangle with one side (other than hypotenuse) of length 4.5 cm.

Q. A triangle $\Delta$ PQR with $\angle Q={90}^{\circ }$, QR = 8 cm and PR = 10 cm is constructed. What would be the measure of PQ?

1. 3 cm
2. 4 cm
3. 10 cm
4. 6 cm

Q. For constructing a triangle, we must know two sides and included angle. Which triangle can be uniquely constructed by knowing two sides and any other angle?

1. None of the above
2. Equilateral triangle
3. Right angled triangle
4. Scalene triangle

Q. In $\Delta$ ABC, the measure of two sides are given and $\angle A$ is a right angle. Which of these properties is used to construct the triangle?

1. S.S.S. property
2. R.H.S. property
3. S.A.S. property
4. A.S.A. property

Q. Steps for the construction of a right triangle LMN in which $\angle M={90}^{\circ }$, MN = 4 cm and LN = 6.2 cm is given below. Choose the correct order.

1. Draw a line segment XY.
2. Construct a line segment MP, sufficiently large such that $\angle NMP={90}^{\circ }$
3. With N as centre and radius 6.2 cm draw an arc, cutting MP at L, join NL.
4. Locate M and N on XY such that MN = 4 cm.

1. 1, 4, 2, 3
2. 1, 4, 3, 2
3. 2, 1, 3, 4
4. 2, 3, 1, 4

Q.

Akash was given lengths of two sides and the measure of an angle which is not included between the two sides. But still he was able to draw the triangle. So what should be the angle that was given? (in degrees)

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Q. A right angled triangle has two equal sides.Both its base angle will be:

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${90}^{\circ }$

Q. A right angled triangle can never be isosceles.

1. True
2. False

Q.

Akash was given lengths of two sides and the measure of an angle which is not included between the two sides. But still he was able to draw the triangle. So what should be the angle that was given? (in degrees)

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