Construction When Two Angles and Included Sides are Given

Q. Steps for the construction of a triangle XYZ, in which XY = 4.5 cm, $\angle X={100}^{\circ }$ and $\angle Y={50}^{\circ }$ is given below. Choose the correct order.

1. Construct a line segment XP such that $\angle PXY={100}^{\circ }$
2. Locate points X and Y on it such that XY = 4.5 cm
3. Draw a line segment which is sufficiently long using ruler
4. Extend XP and YQ to intersect at Z.
5. Construct a line segment YQ such that $\angle XYQ={50}^{\circ }$

1. 3, 2, 5, 1, 4
2. 2, 3, 1, 5, 4
3. 3, 2, 4, 1, 5
4. 2, 1, 3, 4, 5

Q.

Construct $∆\mathrm{ABC}$ with $\mathrm{BC}=7.5\mathrm{cm}$, $\mathrm{AC}=5\mathrm{cm}$ and $\mathrm{m}\angle \mathrm{C}=60°$.

Q.

Raman had to draw an isosceles $△$ABC with base length BC = $5cm$. Which one of the following information is sufficient for him to construct the triangle?

1. base angle is ${65}^{\circ }$
2. Angle other than base angles is ${65}^{\circ }$
3. Median BD is equal to 6cm
4. Median CD is equal to 6cm

Q. Steps for the construction of a triangle XYZ, in which XY = 4.5 cm, $\angle X={100}^{\circ }$ and $\angle Y={50}^{\circ }$ is given below. Choose the correct order.

1. Construct a line segment XP such that $\angle PXY={100}^{\circ }$
2. Locate points X and Y on it such that XY = 4.5 cm
3. Draw a line segment which is sufficiently long using ruler
4. Extend XP and YQ to intersect at Z.
5. Construct a line segment YQ such that $\angle XYQ={50}^{\circ }$

1. 3, 2, 5, 1, 4
2. 2, 3, 1, 5, 4
3. 3, 2, 4, 1, 5
4. 2, 1, 3, 4, 5

Q.

Which of the following concepts plays an important role in angle bisector construction?

1. isosceles triangle

2. congruent triangles

3. equilateral triangles

4. None of these

Q. For the construction of a triangle, we need measures of two angles and ___ side.

1. three
2. two
3. zero
4. one

Q. In $\Delta$ RST, RS = 5 cm, $\angle SRT={45}^{\circ }$ and $\angle RST={45}^{\circ }$. Which criterion can be used to construct $\Delta$RST?

1. A.S.A. criterion
2. S.A.S. criterion
3. S.S.S. criterion
4. A.A.S. criterion

Q. In $\Delta$ RST, RS = 5 cm, $\angle SRT={45}^{\circ }$ and $\angle RST={45}^{\circ }$. Which criterion can be used to construct $\Delta$RST?

1. A.S.A. criterion
2. S.S.S. criterion
3. S.A.S. criterion
4. A.A.S. criterion

Q. One angle of a triangle is 40 degree and the other two angles are equal. Find the measure of the other two angles.

1. 44 degree each
2. 50 degree each
3. 70 degree each
4. 60 degree each

Q.

Which of the following tests cannot be undertaken for checking the construction of triangles?

1. ASA Congruency

2. AAA Congruency

3. SSS Congruency

4. SAS Congruency

Q. Match the following triangles with their appropriate properties.

1. all angles are equal
2. two angles are equal
3. no angle is equal
4. one angle =90 o

Q. Match the postulates of congruency when the given parameters (side 'S' and angle 'A') are satisfied.

1. SSS
2. SAS
3. ASA