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In \(\triangle RST, R = 5 cm, \ and \ \angle{SRT} = 45^{\circ} \ and \ \angle{RST} = 45^{\circ}\). Which criterion can be used to construct ΔRST?
Clearly, from the figure two angles and the included side are given. So, A.S.A. criterion can be used to construct ARST.
Identify the criterion of construction of the equilateral triangle LMN given LM = 6 cm.
Since ALMN is equilateral the measurement of one side is used for the other two sides of the triangle. Hence ALMN can be constructed by S.S.S. criterion.
The idea of equal alternate angles is used to construct which of the following?
A line parallel to a given line.
A Given AB = 3 cm, AC = 5 cm, and \(B = 30^{\circ} , \triangle ABC\) cannot be uniquely constructed, with AC as base, why?
The vertex B cannot be uniquely located.
A line p and a point X not on it are given. Which of the following is used to draw a line parallel to p through X?
Corresponding angles of parallel lines are equal.
ΔPQR is such that P = Q = R = \(60^{\circ}\) which of the following is true?
In ΔPQR since all the angles are acute, it is acute angled. Also since all the angles are equal, it is equilateral
Which vertex of \(\triangle ABC \) is right angled if AB = 8 cm, AC= 6 cm, and BC = 10 cm?
From the given measurements, BC is the hypotenuse. The angle opposite to BC is angle A which is a right angle.
An isosceles triangle is constructed as shown in the figure.
Which of the given statements is incorrect?
Triangle PQR is an equilateral triangle.
\(\triangle PQR \) is constructed with all its angles measuring \(\)60^{\circ} each. Which of the following is correct?
Triangle PQR is an equilateral triangle.
How many perpendicular lines can be drawn to a line from a point not on it?
As can be seen from the given figure, one and only one perpendicular line can be drawn to a given line from a point not on it.
Identify the false statement.
A triangle with two equal sides is called a scalene triangle.
\(\triangle PQR \) is constructed such that PQ = 5 cm, PR = 5 cm and \( \angle{RPQ} = 50^{\circ}\) Identify the type of triangle constructed.
An isosceles as well as an acute angled triangle.
Which of the following is NOT constructed using a ruler and a set square?
A perpendicular bisector of a line segment.
Study the steps of construction given.
Step 1: Draw a ray OA.
Step 2: With O as centre and any convenient radius draw an arc MN to cut OA at M.
Step 3: With M as centre and the same radius draw an arc to cut MN at P.
Step 4: With P as centre and the same radius, draw an arc to cut MN at Q.
Step 5: Draw OQ and produce it to D. An angle AOD is constructed.
What is the measure of angle AOD?
The given steps of construction are to construct an angle of .
In \(\triangle XYZ \), x, y and z denote the three sides. Which of the following is incorrect?
The difference of two sides of a triangle is less than its third side.
In which of the following cases can a triangle be constructed?
Based on the sides of a triangle, which of the following is a classification of triangles?
An isosceles triangle
Which of the following is used to draw a line parallel to a given line?
A line parallel to a given line can be drawn using a ruler and a compass.
Direction: David folds a sheet of paper. The dotted lines as shown in the figure are the creases formed, which are named as l, m and n.
What can you say about lines l and n?
A 90 degree angle is formed at the intersection of l and n.
Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.
The difference of any two sides of a triangle must be less than the third side. This property of triangles is not satisfied by the given measurements as 10 – 7 = 3 > 2 and 10 – 2 = 8 > 7, though 7 – 2 = 5 < 10 is true.
Identify the true statement.
Which of the following statements is incorrect?
A triangular sign board is isosceles. If the unequal side is 7 cm and one of the equal sides is 6 cm, what is the measure of the third side?
6 cm
In the given figure, find the measure of \(\angle{ROT}\), if PQ = QR and \(\angle{QPR} = 60^{\circ} \)
is isosceles since PQ = QR.
∴ is the exterior angle of ΔPQR which is equal to the sum of interior opposite angles .
Which among the following is used to construct a triangle?
S.S.S. criterion can be used indirectly to construct a triangle given the lengths of its three sides.