Construction of a Triangle with RHS Criterion

Q.

A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder. [3 MARKS]

Q. The length and breath of rectangle is 12cm and 5cm respectively. Find the length of diagonals.

Q. The hypotenuse of a triangle is 17 cm long .If one of the remaining two sides is of length 8cm.
Find the length of the third side

Q.

A child walks $6m$ towards the west and then $20m$ in towards south. He then turns east and walks another $12m.$ Then he walks $12m$ towards the north. How far is he from his initial position ?

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

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

Q.

If $\Delta DEF\cong \Delta BCA,$ write the part(s) of $\Delta BCA$ that correspond to

(i) $\angle E$ (ii) $\overline{EF}$ (iii) $\angle F$ (iv) $\overline{DF}$

Q.

The angles of a triangle are in ratio $3:5:7$. Find the measure of each angle of the triangle.

Q.

For constructing $\Delta LMN$ exactly identical to $\Delta ABC$, choose from the options, the minimum measurements required.

1. LM, MN and LN

2. MN and LN

3. LM, MN, LN and ∠MLN

4. LM, MN, LN, ∠MLN and ∠MNL

Q.

The measure of an angle in standard position is given.

Find two positive angles and two negative angles that are co-terminal with the given angle. (Enter your answers as a comma-separated list.)

$-225°$

Q.

Find the measure of each angle of an isosceles triangle if the equal angle measures $15°$ greater than the third angle.

Q. How many unique triangles can be drawn if all the three sides are known?

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

Q.

Construct a right-angled triangle whose hypotenuse is 5 m and one of its lengths is 3 m. [3 MARKS]

Q.

Find all the angles of an equilateral triangle.

Q. Draw the right triangle whose sides are $3cm,4cm$ and $5cm$ and construct its centroid

Q. How long is the hypotenuse of a right triangle if its legs are 3 feet and 4 feet long?

1. 1 Foot
2. 7 Feet
3. 5 Feet
4. 25 Feet

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 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”.

__

Q.

The degree measure of each of the three angles of a triangle is an integer. Which of the following could not be the ratio of their measures?

1. $2:3:4$

2. $3:4:5$

3. $5:6:7$

4. $6:7:8$

Q.

To the nearest second, what is the first time after $12:00$ that the hour hand and the minute hand of a clock are together?

Q.

Identify whether the given statement is true or not ?

$51:58=85:102$

Q.

For constructing $\Delta$LMN exactly identical to $\Delta$ABC, choose from the options, the measurements required.

1. LM, MN, LN and ∠MLN

2. LM, MN and LN

3. MN and LN

4. LM, MN, LN, ∠MLN and ∠MNL

Q. Which congruence criterion do you use in the following?
Given: EB = BD, AE = CB, $\angle A=\angle C={90}^{\circ }$

Q. Construct a right triangle whose base is 7.5 cm. and sum of its hypotenuse and other side is 15 cm.

Q. Construct a right-angled triangle the length of whose hypotenuse is $5$ cm and one of the remaining side is $3$ cm long.

Q.

A triangle is constructed by joining the minute's hand position when it was showing 12 and 3. Find the angle between the positions and what type of triangle is it? [1 MARK]

Q.

Pavan followed the steps given below to construct a triangle

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

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

Are the steps followed by him correct?

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

__

Q. Which congruence criterion do you use in the following?
Given: EB = BD, AE = CB, $\angle A=\angle C={90}^{\circ }$

Q. Which congruence criterion do you use in the following?
Given: EB = DB
AE = BC
$\angle A=\angle C={90}^{\circ }$
So, ΔABE ≅ ΔCDB

Q.

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

1. Isosceles triangle

2. Equilateral triangle

3. Right angled triangle

4. Scalene triangle

Q. ______ triangle can be uniquely constructed by knowing two sides and any other angle.

1. Isosceles
2. Equilateral
3. Right angled
4. Scalene