Construction of Triangle 2

Q. Question 4
Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1.5 times the corresponding sides of the isosceles triangle.

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. Try to construct a triangle with sides 5 cm, 8 cm and 1 cm. Is it possible or not ? Why ? Give your justification.

Q. To construct a triangle, the difference between any two sides must be _______ the third side.

1. greater than or equal to
2. greater than
3. lesser than
4. equal to

Q.

To construct a triangle given its base, a base angle and the difference of the other two sides, there is only a single type of construction.

1. True

2. False

Q.

How will you prove that the construction for a triangle with the given conditions is right?

Given conditions: Base length BC is given, base angle B is given, and difference of the other two sides is given (AB-AC) where AB is greater than AC. For going about the construction, I drew the base length BC, drew the ray BX with angle XBC known to me. Taking B as centre and radius equal to (AB-AC) I cut an arc on the ray BX intersecting it at point D. I then joined D to C. Then drew the perpendicular bisector of the line segment DC and named the point of intersection of this perpendicular bisector and the ray BX as A. Joined A to C and the triangle ABC was ready

Which of the following statements gives the best explanation to this construction?

1. Since the triangles AMD and AMC are congruent, AD = AC and hence the location of A has been plotted correctly

2. the triangles DBC and CAD are congruent the location of A is justified

3. AM is the altitude for the triangle ADC and hence the location of A is justified

4. None of these

Q. Construct a $\Delta ABC$ in which $BC=5.6cm,AC–AB=1.6cmand\angle B={45}^o$.

Q.

Construct a triangle ABC, in which $\angle$B = 53.13°, $\angle$C = 36.87° and AB + BC+ CA = 24 cm. What type of triangle is this? [4 MARKS]

Q. In construction of a triangle ABC in which BC = 6 cm, $\angle B={45}^{\circ }$ and AB - AC = 2.5 cm, how many perpendicular bisectors are drawn?

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

Q.
In the figure, if $AM$ is the perpendicular bisector of $CD$, is equal to $AC-AB$.

1. AD
2. BD
3. DM
4. BM

Q.

Construct a triangle ABC in which BC is 5 cm, Angle B is ${60}^{\circ }$ and AB-AC=0 cm. What type of triangle is this?

Q. $△ABC$ and $△DBC$ are two isosceles triangles on the same base $BC$ and vertices $A$ and $D$ are on the same side of $BC$. If $AD$ is extended to intersect $BC$ at $P$, show that
(i) $△ABD\cong △ACD$
(ii) $△ABP\cong △ACP$
(iii) $AP$ bisects $\angle A$ as well as $△D$.
(iv) $AP$ is the perpendicular bisector of $BC$.

Q.

Construct a triangle with sides $5cm,6cm$ and $7cm$ and then another triangle whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.

Q. In $△$ABC, AB = AC and AD is perpendicular bisector of BC. The property by which $△$ADB is not congruent to $△$ADC is ______.

1. SAS property
2. SSS property
3. RHS property
4. AAA property

Q.

Construct a triangle ABC, in which $\angle$B = 53.13°, $\angle$C = 36.87° and AB + BC+ CA = 24 cm. What type of triangle is this? [4 MARKS]

Q. Suppose $△ABC$ has to be constructed in such a way that $BC=5$ cm, $\angle ABC={30}^{\circ }$ & $AB-AC=0$. The triangle is a/an triangle.

1. equilateral
2. scalene
3. isosceles
4. right-angled

Q.

In the given figure $AD$ is the bisector of $\angle A$ and $AB=AC.$ Then $△ACD$ and $△ADB$ are congruent by which criterion?

1. $ASA$

2. None of these

3. $SSS$

4. $SAS$

Q. How many arcs are drawn to construct a triangle PQR in which $QR=6cm,\angle Q={60}^{\circ }andPR-PQ=2cm$.

1. 2
2. 4
3. 7
4. 6

Q.

$\Delta$ ABC is an isosceles triangle with AB = AC. Side BA is produced to D such that AB = AD. Prove that $\angle$BCD is right angle. [4 MARKS]

Q. The construction of a $\Delta ABC$ in which AB = 7 cm, $\angle A={75}^{\circ }$ is not possible when the difference of BC and AC is equal to

1. 6.5 cm
2. 6 cm
3. 5.5 cm
4. 7.6 cm

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. How many arcs are drawn to construct a triangle PQR in which $QR=6cm,\angle Q={60}^{\circ }andPR-PQ=2cm$.

1. 2
2. 4
3. 6
4. 7

Q. In construction of a triangle ABC in which BC = 6 cm, $\angle B={45}^{\circ }$ and AB - AC = 2.5 cm, how many perpendicular bisectors are drawn?

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

Q. To construct a $\Delta PQR$, in which QR= 5.5 cm, $\angle Q={60}^{\circ }$ and PR - PQ = 2.5 cm, the steps of construction are given below. Complete the third step

Here, PR > PQ,
i.e., the side containing base angle is less than the third side.

Steps of construction:
Step 1: Draw the base QR = 5.5 cm
Step 2: At the point Q, make an $\angle XQR={60}^{\circ }$
Step 3 will be

1. Cut line segment QS = PR - PQ = 2 cm from the line QX extended on opposite side of linesegment QR
2. Cut line segment QS = PR - PQ = 2.5 cm from the line QX extended on opposite side of line segment QR
3. Cut line segment QS = PR - PQ = 2.5 cm from the ray QX
4. Draw the perpendicular bisector LM of SR.

Q. Triangle ABC is constructed with AB = 4 cm, ∠CAB = ${45}^0$ and BC = 2.92 cm. Draw two perpendicular bisectors of side AB and BC. These two bisectors will intersect at a point. State whether True or False.

1. True
2. False

Q. How many arcs are drawn to construct a triangle PQR in which $QR=6cm,\angle Q={60}^{\circ }andPR-PQ=2cm$.

1. 2
2. 4
3. 7
4. 6

Q. $\text{A unique}△ABC\text{can be}\text{constructed, if the values of}\text{AC, AB - BC and}\angle A\text{are given.}$

1. False
2. True