Is it possible to construct a unique triangle ΔABC with the following
measurements:
AB =5 cm, BC=4 cm, AC=1 cm.
Justify your answer.
Answers
Step-by-step explanation:1. Draw a line segment BC = 6 cm. 2. Taking B and C as centres, draw two arcs of radii 4 cm and 9 cm intersecting each other at A. 3. Join BA and CA, ΔABC is the required triangle. 4. From B, draw any ray BX downwards making an acute angle. 5. Mark three points B1, B2, B3 on BX, such that BB1 = B1B2 = B2B3. 6. Join B2C and from B3 draw B3M || B2C intersecting the extended line segment BC at 7. From point M, draw MN||CA intersecting the extended line segment BA to N. Then, ΔNBM is the required triangle whose sides are equals to of the corresponding sides of the ΔABC The two triangles are not congruent because, if two triangles are congruent, then they have same shape and same size. Here, all the three angles are same but three sides are not same one side is different. Justification: Read more on Sarthaks.com - https://www.sarthaks.com/886112/draw-abc-in-which-ab-cm-bc-cm-and-ac-cm-construct-triangle-similar-to-abc-with-scale-factor