# Construction of Triangle 2

## Trending Questions

**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 ΔABC in which BC = 5.7 cm, ∠B=60∘ 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 ∠YBC=60∘

Step 2: Cut the line segment BD = 3 cm from the ray BY.

Step 3 will be

- Let PQ intersect BX at A.Then, join AC
- Join DC and draw PQ⊥BY
- Join DC and draw PQ⊥DC
- Join DC and draw PQ⊥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.

- greater than or equal to
- greater than
- lesser than
- 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.

True

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?

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

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

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

None of these

**Q.**Construct a ΔABC in which BC=5.6cm, AC–AB=1.6cmand∠B=45o.

**Q.**

Construct a triangle ABC, in which ∠B = 53.13°, ∠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, ∠B=45∘ and AB - AC = 2.5 cm, how many perpendicular bisectors are drawn?

- 1
- 3
- 2
- 4

**Q.**

In the figure, if AM is the perpendicular bisector of CD,

- AD
- BD
- DM
- BM

**Q.**

Construct a triangle ABC in which BC is 5 cm, Angle B is 60∘ 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≅△ACD

(ii) △ABP≅△ACP

(iii) AP bisects ∠A as well as △D.

(iv) AP is the perpendicular bisector of BC.

**Q.**

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 75 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 ______.

- SAS property
- SSS property
- RHS property
- AAA property

**Q.**

Construct a triangle ABC, in which ∠B = 53.13°, ∠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, ∠ABC=30∘ & AB−AC=0. The triangle is a/an

- equilateral
- scalene
- isosceles
- right-angled

**Q.**

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

ASA

None of these

SSS

SAS

**Q.**How many arcs are drawn to construct a triangle PQR in which QR=6 cm, ∠Q=60∘ and PR−PQ=2 cm.

- 2
- 4
- 7
- 6

**Q.**

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

**Q.**The construction of a ΔABC in which AB = 7 cm, ∠A=75∘ is not possible when the difference of BC and AC is equal to

- 6.5 cm
- 6 cm
- 5.5 cm
- 7.6 cm

**Q.**Construct a triangle ABC in which BC = 6 cm, ∠B=45∘ and AB - AC = 2.5 cm

Steps of construction:

Step 1: Draw BC = 6 cm

Step 2: Construct ∠YBC=45∘

Step 3 will be -

- Join AC, ΔABC is the required triangle.
- Draw perpendicular bisector of CD intersecting BY at A.
- From ray BY, cut-off line segement BD = 2.5 cm
- Join CD

**Q.**How many arcs are drawn to construct a triangle PQR in which QR=6 cm, ∠Q=60∘ and PR−PQ=2 cm.

- 2
- 4
- 6
- 7

**Q.**In construction of a triangle ABC in which BC = 6 cm, ∠B=45∘ and AB - AC = 2.5 cm, how many perpendicular bisectors are drawn?

- 1
- 2
- 3
- 4

**Q.**To construct a ΔPQR, in which QR= 5.5 cm, ∠Q=60∘ 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 ∠XQR=60∘

Step 3 will be

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

**Q.**Triangle ABC is constructed with AB = 4 cm, ∠CAB = 450 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.

- True
- False

**Q.**How many arcs are drawn to construct a triangle PQR in which QR=6 cm, ∠Q=60∘ and PR−PQ=2 cm.

- 2
- 4
- 7
- 6

**Q.**A unique △ABC can be constructed, if the values of AC, AB - BC and ∠A are given.

- False
- True