Triangle Similarity Proof: Comparing Triangles ABD and ADC with Heights of 7 and 15 Units

AAABBBCCCDDD15157 Are triangles ΔABD and ΔADC similar?

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Step-by-step video solution

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00:00 Are the triangles similar?
00:03 The triangle is isosceles according to the given data
00:08 In an isosceles triangle, the height is also a median (T)
00:15 Legs are equal in an isosceles triangle (T)
00:23 Common side between the triangles (T)
00:29 The triangles are congruent by SAS
00:35 Congruent triangles are necessarily similar
00:38 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

AAABBBCCCDDD15157 Are triangles ΔABD and ΔADC similar?

2

Step-by-step solution

Since side AB is equal to side AC, the triangle is isosceles.

AD divides BC into two equal parts, therefore BD = DC.

Also, AD is a common side.

From this, it follows that the triangles are similar according to the S.S.S (side side side) criterion.

3

Final Answer

Yes, according to S.S.S.

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