HL Triangle Construction

HL Triangle Construction (RHS triangle Construction) : A triangle is said to be a right triangle, if one of its three angles is a right angle.

To construct a right triangle ABC right angled at C when its hypotenuse is AC and one side is BC is given, we follow the following steps :

Step 1 : Draw a line segment BC of given length.

Step 2: Draw ∠BCX of measure 90 0 .

Step 3 : With center B and radius equal to the hypotenuse AB, draw an arc of the circle to intersect ray CX at A.

Step 4 : Join BA to obtain the required triangle ABC.


RHS Triangle Construction

Construct a right triangle PQR in which ∠Q = 90
0 , PR = 6 cm and QR = 4 cm.

Step 1: Draw QR = 4 cm.

Step 2 : Using compass, at Q draw ∠RQK = 90
0 .

Step 3 : Cut off RP = 6 cm.

Step 4 : Join P and R.

Now we get the required ΔPQR.

Practice Problems

1) If the sides of triangle are 3cm,4cm and 5cm then what type of triangle you will get after constructing it?

2) Construct a right angled triangle ABC where AB = 4.5 cm, AC = 5.8 cm and angle A = 90
0 .

3) In a triangle PQR, if ∠P=90
0 and ∠Q= ∠R, find the angles of the triangle .

Geometrical Constructions

Basic Geometric Constructions
Construction of Line Segment
Bisecting a Line Segment
Constructing Angles
Bisecting Angles
Constructing Parallel Lines
Construction of Triangle (SSS)
SAS Triangle Construction
ASA Triangle Construction
HL Triangle Construction (Rhs -construction)
Constructing Quadrilaterals
Constructing Triangles(when sum of sides or perimeter is given)

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