Construction of a Triangle Abc with Given Base, Base Angle and Difference between Two Sides AB & AC, with AB > AC

Q.

maithili , shaila and ajay live in three different places in the city . A toy shop is equidistant from the 3 houses. which geometrical construction should be used to represent this? explain the answer

Q.

For the construction of a circumcircle of a triangle, we take angle bisector of any two angles of a triangle. State whether the given information is true or false.

1. True

2. False

Q.

What is the last step in constructing quadrilateral with 3 sides and 2 included angles given?

1. Draw line segment

2. Mark the vertices

3. Draw arc

4. Construct triangle

Q.

(a) Construct a right-angled triangle with hypotenuse 7.6 cm and one of the sides 5.2 cm.

(b) Construct ΔABC, where AB = 6 cm, BC = 7 cm and CA = 9 cm. Is it a right angled triangle? [4 MARKS]

Q. How to construct a triangle with SAS, ASA, SSS and RHS

Q.

Construct a triangle ABC, in which AB = 5.6 cm and AB = BC, ∠B = 60°.

Q.

A triangle ABC in which BC = 3.4 cm, AB - AC = 1.5 cm and DB = 45${}^{\circ }$ can be constructed using compass and ruler.

1. True
2. False

Q.

How many arcs are need to be drawn using the method of Triangle Construction 2?

1. 2

2. 3

3. 4

4. 1

Q. Construct a triangle ABC in which BC = 6 cm, $\angle B={45}^{\circ }$ and AB - AC = 2.5 cm

Steps of construction:
Step 1: Draw BC = 6 cm
Step 2: Construct $\angle YBC={45}^{\circ }$
Step 3 will be -

1. Join AC, $\Delta ABC$ is the required triangle.
2. Draw perpendicular bisector of CD intersecting BY at A.
3. From ray BY, cut-off line segement BD = 2.5 cm
4. Join CD

Q.

Which of the following congruencies could be the test for the construction of triangles where there is base length given, one of the base angles is given and the difference between the other two sides of the triangle are given?

1. SSS Congruency

2. RHS Congruency

3. None of these

4. ASA Congruency

Q. To construct a $\Delta ABC$ in which BC = 5.7 cm, $\angle B={60}^{\circ }$ and AB - AC = 3cm, the steps of construction are given below.

Here, AB > AC, i.e. the side containing the base angle B is greater than third side
Steps of construction:
Step 1: Draw the base BC = 5.7 cm and draw a ray BY making an $\angle YBC={60}^{\circ }$
Step 2: Cut the line segment BD = 3 cm from the ray BY.
Step 3 will be

1. Let PQ intersect BX at A.Then, join AC
2. Join DC and draw $PQ\perp BY$
3. Join DC and draw $PQ\perp DC$
4. Join DC and draw $PQ\perp BC$

Q.

The steps to draw a triangle with the base BC, a base angle $\angle$B and the difference of other two sides is given below.
1. Draw the base BC and at point B make an angle say XBC equal to the given angle.
2. Cut the line segment BD equal to AB - AC on the reflection of ray BX (i.e. BX').
3. Join DC and draw the perpendicular bisector, say PQ of DC.​​
The next step will be:

1. 1, 4, 3, 2

2. 1, 4, 2, 3

3. 1, 3, 2, 4

4. 1, 2, 3, 4

Q.

For constructing a triangle with a given base, a base angle and difference between the other two sides, a ___ bisector is required.