Construction of Triangles When Two Angles and one included Side is Given

Q.

Question 1
Construct $\Delta$ DEF such that DE = 5 cm, DF = 3 cm and $\angle$ EDF = ${90}^{\circ }$

Q. A triangle can be constructed if the measure of two angle and side is given

1. included
2. non-included
3. adjacent
4. opposite

Q. Steps of construction of triangle from two angles of 60${}^{\circ }$ and 30${}^{\circ }$ and included side of 4 cm

1. $Mark60degreesatA$
2. $MarkintersectionasC$
3. $Mark30degreesatB$
4. $DrawlineABof4cm$
5. Join A, C and B, C

Q. Question 1
Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and, say why you cannot construct them. Construct rest of the triangle.
$\begin{array}{ccccc}& Triangle& & Givenmeasurements& \\ 1.& \Delta ABC& m\angle A={85}^{\circ }& m\angle B={115}^{\circ }& AB=5cm\end{array}$

Q. $△$ABC is constructed such that BC = 5.8 cm, $\angle$C= $\angle$B = 30${}^{\circ }$. Then, the sum of length of side AC and AB is

1. 6.8 cm
2. 5.4 cm
3. 7.2 cm
4. 4.8 cm

Q. Construct $\Delta PQR$, given $\overline{PQ}=3.5cm,\overline{PR}=3cm$, and $\angle RPQ={120}^{\circ }$ [4 MARKS]

Q.

(a) 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?
(b) Which of the following congruency conditions is preferred to draw a triangle exactly congruent to a right-angled triangle? [2 MARKS]

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. ∆ABC is constructed such that AB = 7 cm, AC = 4 cm and ∠A = 75⁰. Then find the length of side BC.

Q. ∆ABC is constructed such that AB = 7 cm, AC = 4 cm and ∠A = 75⁰. Then find the length of side BC.

Q. Given below are different measurement of a triangle and one of their construction step. Match the correct pair

1. Draw two arcs
2. Mark two degrees
3. Draw one arc
4. Draw a right angle

Q. $△$ABC is drawn with the length of side AB being 7 cm. If $\angle$A is 63${}^{\circ }$ and $\angle$C is 57${}^{\circ }$, then, which of the following should be the starting step for drawing this triangle ABC.

1. Mark 63 degrees at point A
2. Calculate value of angle B
3. Mark 57 degree at point C
4. Draw a line segment AC of 7 cm

Q. △ABC is drawn with the length of side BC being 9.6 cm. If ∠C is ∠36⁰ and B is 84⁰, then, what is the length of side AB? ( in cm)

1. 7.6 cm
2. 6.6 cm
3. 8.6 cm
4. 5.6 cm

Q. ∆XYZ is constructed such that XY = 4 cm, XZ = 8 cm and ∠X = 20⁰. Then, find the sum of measures of ∠Y and ∠X.

Q. Steps of construction of triangle from two angles of 60${}^{\circ }$ and 30${}^{\circ }$ and included side of 4 cm

1. $Mark60degreesatA$
2. $MarkintersectionasC$
3. $Mark30degreesatB$
4. $DrawlineABof4cm$
5. Join A, C and B, C

Q. ∆XYZ is constructed such that XY = 4 cm, XZ = 8 cm and ∠X = 20⁰. Then, find the sum of measures of ∠Y and ∠X.

Q. Steps of construction of triangle from two angles of 60${}^{\circ }$ and 30${}^{\circ }$ and included side of 4 cm

1. $Mark60degreesatA$
2. $MarkintersectionasC$
3. $Mark30degreesatB$
4. $DrawlineABof4cm$
5. Join A, C and B, C

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.

$△$DEF is drawn with the length of side EF being 7.5 cm. If $\angle$E is 75${}^{\circ }$ and $\angle$F is 55${}^{\circ }$, then the measure of $\angle$D is

1. 40${}^{\circ }$

2. 30${}^{\circ }$

3. 50${}^{\circ }$

4. 20${}^{\circ }$

Q.

$△$ABC is drawn with the length of side AB being 6 cm. If $\angle$A is 65${}^{\circ }$ and $\angle$B is 65${}^{\circ }$, then $△$ABC is

1. an equilateral triangle

2. a scalene triangle

3. an isosceles triangle

4. an obtuse angled triangle

Q.

$△$XYZ is drawn with the length of side XZ being 4.7 cm. If $\angle$X is 80${}^{\circ }$ and $\angle$Z is 65${}^{\circ }$, then, the measure of $\angle$Y and the length of side YZ respectively are

1. 35${}^{\circ }$, 8 cm

2. 35${}^{\circ }$, 7.4 cm

3. 45${}^{\circ }$, 8 cm

4. 45${}^{\circ }$, 7.4 cm

Q.

$△$PQR is drawn with the length of side QR being 4 cm. If $\angle$Q is 35${}^{\circ }$ and $\angle$R is 70${}^{\circ }$, then, the length of the side PR is

1. 4 cm

2. 3.6 cm

3. 2.9 cm

4. 2.4 cm

Q.

$△$ABC is drawn with the length of side BC being 9.6 cm. If $\angle$C is 36${}^{\circ }$ and $\angle$B is 84${}^{\circ }$, then, the length of side AB is

1. 11 cm

2. 9.8 cm

3. 6.6 cm

4. 5.4 cm

Q.

$△$ABC is drawn with the length of side AB being 4.8 cm. If $\angle$B is 35${}^{\circ }$ and $\angle$C is 65${}^{\circ }$, then, the perimeter of this triangle is

1. 20.4 cm

2. 19.8 cm

3. 18.2 cm

4. 21.1 cm

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. Either length of one side or measure of one angle

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

3. Length of the third side

4. Measure of one angle