Construction of a Triangle with ASA Criterion

Q.

In which of the following cases, a unique triangle can be drawn .

1. $\mathrm{AB}=4\mathrm{cm},\mathrm{BC}=8\mathrm{cm},\mathrm{CA}=2\mathrm{cm}$

2. $\mathrm{BC}=5.2\mathrm{cm},\angle \mathrm{B}=90°,\angle \mathrm{C}=110°$

3. $\mathrm{XY}=5\mathrm{cm},\angle \mathrm{X}=45°,\angle \mathrm{Y}=60°$

4. An isosceles triangle with the length of each equal side $6.2\mathrm{cm}$.

Q. How we are getting angles $\angle 1+\angle 2+\angle 3=180$

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

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

Q.

Given below is a line segment. Draw one line segment congruent to it

Q. Construct $\Delta$KLM such that KL = 9 cm, KM = 8 cm, and $\angle K$ = 35°. Find the length of LM.

1. 4.2 cm
2. 5.2 cm
3. 5.7 cm
4. 6.2 cm

Q. Construct a ΔABC in which BC = 6 cm, ∠B = ${35}^{\circ }$and ∠C = ${100}^{\circ }$

Q.

Raman had to draw an isosceles triangle with base angles as ${65}^{\circ }$ each and base length of $5cm$. Raman said the given data is insufficient. Is he correct?

1. True

2. False

Q.

Is it possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD = 7cm , $\angle$ABC = ${45}^{\circ }$ and $\angle$BCD = ${55}^{\circ }$?

1. Yes, it is possible

2. No, it is impossible

3. With the measure of a diagonal, yes​

4. With the measure of an extra side, yes

Q. how to know that the triangle is acute obtuse or right angled if value of three sides is given

Q.

Construct $△\mathrm{ABC}$ in which $\mathrm{BC}=6.2\mathrm{cm}$, $\angle \mathrm{B}=45°$, $\angle \mathrm{A}=35°$. Measure $\angle \mathrm{C}$. What kind of this triangle is this?

Q. Construct $\Delta$ PQR if PQ=5cm, $\angle PQR={105}^{\circ }and\angle QRP={35}^{\circ }$.

Q. Construct a triangle $PQR$ in which $QR=7cm,\angle Q={75}^o$ and $PQ+PR=13cm$

Q. Construct a $△PQR$ such that $\angle P={30}^{\circ },\angle Q={60}^{\circ }$ and $PQ=10cm$.

Q.

3 sides and any 2 angles are sufficient to construct a quadrilateral.

1. True

2. False

Q. Construct a triangle of whose side lengths are $4\text{cm},5\text{cm},7\text{cm}.$

Q. Construct $\Delta$XYZ such that XY = 8 cm, $\angle X$ = 40°, and $\angle Y$ = 95°. Find the length of YZ.

1. 8.3 cm
2. 7.3 cm
3. 8.8 cm
4. 9.3 cm

Q.

Construct $△HAT$ such that $HA=AT=5cm$ and$\angle A=60°$. What are the measures of other two angles of the triangles? What type of triangle is this?

Q. Which of the following steps is INCORRECT while constructing $△XYZ$ if it is given that $XY=6cm,\angle ZXY={30}^o$ and $\angle XYZ={100}^o$
Step 1: Draw line $XY$ of length $6cm$.
Step 2: At $X$, draw a ray $XP$ making an angle of ${30}^o$ with $XY$.
Step 3: At $Y$, draw a ray $YQ$ making an angle of ${100}^o$ with $YX$.
Step 4: The point of intersection of the two rays $XY$ and $YQ$ is $Z$.

1. Step 1
2. Step 2 and Step 4
3. Step 3
4. Step 4

Q.

Construct:

$\Delta PQR$ if $PQ=5cm$, $\angle PQR={105}^{\circ }$ and $\angle QRP={40}^{\circ }$.
(Hint : Recall angle-sum property of a triangle),

Q.

Fill $can/cannot$in the given blank.

We ________ construct a triangle $∆PQR$when $PQ=7.2cm,$$m\angle R={60}^o$and $PR=5.7cm$

Q. Construct $\Delta$ PQR if PQ=5cm, $\angle PQR={105}^{\circ }and\angle QRP={35}^{\circ }$.

Q.

1. 1
2. 2
3. 3
4. none of these

Q. Construct a triangle $XYZ$ in which $XY=4.5cm$ and $\angle X={100}^{\circ }$ and $\angle Y={50}^{\circ }$ using ruler and protractor.

Q.

Which of the following data is not sufficient to draw a unique triangle?

1. Side, Side, Angle

2. Side, Angle, Side

3. Angle, Angle, Angle

4. Angle, Angle, Side

Q.

1. 1
2. 2
3. none of these
4. 3

Q. Construct a triangle $ABC$ in which $AB=6.5cm,\angle A={45}^{\circ }$ and $\angle B={60}^{\circ }$

Q. Construct an equilateral triangle whose sides are of length $5.5$ cm.

Q. Construct a triangle $△MNO$ where $\angle M={70}^o,\angle N={60}^o$ and side $MN=7cm$.

Q.

Raman had to draw an isosceles triangle with base angles measuring ${65}^{\circ }$ each and base length of $5cm$. Raman said the given data is insufficient. Is he correct?

1. True

2. False

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