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Standard IX

Mathematics

Proof for Validation for Construction of a Triangle with Given Perimeter and Two Base Angles

How many tria...

Question

How many triangles are there in the adjacent figure?

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Solution

After labeling the figure as shown below and count the triangles. There are 19 triangles.
$△ A E H, △ A E B, △ E B F, △ A B H, △ B H I, △ F G I, △ G J C, △ G I C, △ G I J, △ B I C, △ A J C, △ C I J,$
$△ C J D, △ J D K, △ A J H, △ A J D, △ E H J, △ F I J, △ A F B, △ A G C$

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Q. How many triangles are there in the figure?

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How many triangles are there in the adjacent figure?

After labeling the figure as shown below and count the triangles. There are 19 triangles.△AEH,△AEB,△EBF,△ABH,△BHI,△FGI,△GJC,△GIC,△GIJ,△BIC,△AJC,△CIJ,△CJD,△JDK,△AJH,△AJD,△EHJ,△FIJ,△AFB,△AGC