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 90⁰.

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.




Example

RHS Triangle Construction

Construct a right triangle PQR in which ∠Q = 90⁰, PR = 6 cm and QR = 4 cm.

Step 1: Draw QR = 4 cm.

Step 2 : Using compass, at Q draw ∠RQK = 90⁰.

Step 3 : Cut off RP = 6 cm.

Step 4 : Join P and R.

Now we get the required ΔPQR.


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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 = 90⁰.

3) In a triangle PQR, if ∠P=90⁰ and ∠Q= ∠R, find the angles of the triangle .

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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)

Geometry

7th grade Math

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