Construction of a Triangle with SSS Criterion

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Question 4
Construct $\Delta$ ABC such that AB = 2.5 cm, BC = 6cm and AC = 6.5 cm. Measure $\angle$ B.

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Question 99
Draw a triangle whose sides are of lengths 4 cm, 5 cm and 7 cm.

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Question 3
Draw $\Delta$ PQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?

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Question 1
Construct $\Delta$ XYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.

Q.

If under a given correspondence, the three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent by which condition?

1. ASA

2. RHS

3. SSS

4. SAS

Q. Question 2
Construct an equilateral triangle of side 5.5 cm.

Q. In triangles ABC and PQR, AB = PQ, BC = QR and CA = RP, then by which congruency criteria are these two triangles congruent?

1. A.S.A. criterion
2. A.A.A. criterion
3. S.S.S. criterion
4. S.A.S. criterion

Q.

Question 100
Construct an obtuse-angled triangle which has a base of 5.5 cm and base angles of ${30}^{\circ }$ and ${120}^{\circ }$.

Q. If 4 cm, 8 cm, and 2 cm are the measures of three lines segment, can it be used to draw a triangle?

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Construct a triangle PQR in which PQ = 5 cm, PR = 3 cm and ∠P = 30°.

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Construct a triangle LMN, given LM = 5 cm, MN = 6.8 cm and ∠LMN = 70°. Write the steps of construction.

Q. In the given right angled triangle, find the length of AC.

1. 14 cm
2. 12 cm
3. 13 cm
4. 15 cm

Q.

If the sides of a triangle are $\text{39 cm, 80 cm, and 89 cm}$, then the triangle formed is a right-angled triangle.

1. Obtuse-angled

2. Right-angled

Q. Construct triangles of the measures given below.
In ∆SAT, l(AT) = 6.4 cm, m ∠A = 45^°, m ∠T = 105^°

Q.

A triangle having all sides of different lengths is called …………… triangle.

1. a scalene

2. an isosceles

3. an equilateral

4. an acute

Q. Construct triangles of the measures given below.

Q.

The line segment BD = ________ in the given diagram.

1. AB + AC

2. AB - AC

3. AD

4. AC - AB

Q.

If 2 angles of a triangle are congruent, what type of triangle it is?

Q. Question 7
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.
$\begin{array}{ccccc}& Triangle& & Givenmeasurements& \\ 7.& \Delta XYZ& XY=3cm& YZ=4cm& XZ=5cm\end{array}$

Q.

Construct a triangle DEF, in which EF = 4.5 cm, DF = 6.8 cm, ∠F = 110°.

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A $∆ABC$can be constructed when $AC=8cm,$$m\angle A={60}^o$and $m\angle B={50}^o$using the _________ criterion.

1. $ASA$

2. $SAS$

Q. Identify the criterion of construction of the equilateral triangle ABC given AB = 9 cm.

1. S.A.S. criterion
2. R.H.S. criterion
3. A.S.A. criterion
4. S.S.S. criterion

Q.

Construct $∆PQR$ if $PQ=5\mathrm{cm},\mathrm{m}\angle PQR={105}^{°}\mathrm{and}\mathrm{m}\angle QRP={40}^{°}$. (Hint: Recall the angle-sum property of a triangle).

Q.

A student was given the following details while constructing a triangle ABC:

The length of the base of the triangle BC, one of the base angles say $\angle$ B and the sum of the other two sides of the triangle (AB+AC)

He went about the construction of this triangle by first drawing the base of the triangle BC. He then drew an angle at the point B equal to the given angle on a ray that he drew. After completing these steps, he got stuck and doesn’t know what to do next. Which of the following steps will he take up next?

1. Cut a line segment BD equal to (AB+AC) on that same ray

2. Change the base length to (AB+AC) and then draw one of the base angles at one of the ends of the line segment whose length is equal to (AB+AC)

3. Cut a line segment BD equal to $2(AB+AC)$ on that same ray

4. He knows the perimeter of the triangle, he changes the base length to that of the perimeter of the triangle and then draws one of the base angles at one of the ends of the line segment

Q. A triangle having sides measuring 5 cm, 11 cm and 13 cm is a _______ triangle.

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

Q.

Goutham has been asked to draw a triangle with three lengths given to him. He hasn't checked the given lengths and promised that he will draw the triangle thinking that a triangle can always be constructed with any three lengths. Is it true that a triangle can always be constructed with any three lengths?

1. False

2. True

Q.

Construct the right angled ΔPQR, where m∠Q = 90°, QR = 8 cm and PR = 10 cm.

Q. Draw a triangle of perimeter 13 𝑐𝑚 and sides in the ratio 3:4:5.

Q. How to construct a triangle wirh PQ=8cm, QR=2cm and RP=4cm

Q.

Construct a triangle XYZ, given XY = 4.2 cm. YZ = 5.3 cm and ∠Y = 55°.