एक त्रिभुज की रचना करना जिसका परिमाप और आधार के कोण दिए हैं।
हमें एक ऐसे त्रिभुज की ABC कि रचना करनी है जिसका परिमाप (तीनों भुजाओं की लंबाई का योग) और त्रिभुज के आधार के दोनों कोणों की माप दी गयी है। माना कि त्रिभुज ABC का परिमाप(AB + Bc + CA) 10 सेमी है और आधार के दो कोण क्रमश: 45° और 60° के हैं। इस त्रिभुज की रचना के निम्न चरण हैं :
चरण 1 – त्रिभुज के परिमाप 10 सेमी के बराबर एक रेखाखण्ड PQ खींचिए।
चरण 2 – बिन्दु P पर दिए गए आधार का एक कोण (45° का) बनाईये।
चरण 3 – बिन्दु Q पर दिए गए आधार का दूसरा कोण (60° का) बनाईये।
चरण 4 – चरण 2 और चरण 3 में बने कोणों के अर्धक बनाईये।
चरण 5 – दोनों कोण अर्धकों के प्रतिच्छेद बिन्दु A को अंकित करें।
चरण 6 – AP और AQ के लंब-समद्विभाजक बनाईये।
चरण 7 – AP के लंब-समद्विभाजक और PQ के प्रतिच्छेद बिन्दु B तथा AQ के लंब-समद्विभाजक और PQ के प्रतिच्छेद बिन्दु C को अंकित करें।
चरण 8 – A से बिन्दु B और बिन्दु C को मिलाइये। इस प्रकार बना त्रिभुज ABC वान्छित त्रिभुज है।
STEP स्लाईडर के उपयोग से त्रिभुज की रचना के विभिन्न चरण देखे जा सकते हैं।
Construction of a triangle whose perimeter and base angles are given.
We need to construct a triangle ABC whose perimeter (sum of lengths f two sides) and measure of two base angles are given. Let the perimeter (AB+BC+CA) of the triangle ABC be 10 cm and the measure of two base angles are 45° and 60°. The construction can be completed in the following steps:
Step 1 – Draw a line segment of 10 cm length equal to the perimeter of the triangle.
Step 2 – Make an angle of 45° at point P.(one of the given angles)
Step 3 – Make an angle of 60° at point Q.(second given angle)
Step 4 – Construct the angle bisectors of angles of step 2 and step 3.
Step 5 – Mark the point of intersection of two angle bisectors.
Step 6 – Construct the perpendicular bisectors of AP and AQ.
Step 7 – Mark point B, the point of intersection of the perpendicular bisector of AP and PQ. Similarly mark point C, the point of intersection of the perpendicular bisector of AQ and PQ.
Step 8 – Join A to point B and point C. The triangle ABC thus formed is the required triangle.
Slider STEP can be used to see the different steps of construction of the triangle.
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