Prove that the medians corresponding to equal sides of an isosceles triangle
are equal.
YALGAAR HO!
Answers
Answer:
Step-by-step explanation:
We have to prove that BD = CE when AB = AC. ( where BD and CE are the medians)
In ∆ ABC
AB = AC ( Isosceles ∆)
∠B = ∠C…………..(1)
[ANGLE OPPOSITE TO EQUAL SIDES ARE EQUAL]
AB = AC
1/2 AB = 1/2 BC
BE = CD…………(2)
( as BD and CE are the medians of a triangle)
In ΔEBC & ΔDCB
∠B = ∠C ( From eq I)
BC = CB (Common)
BE= CD (From eq 2)
ΔEBC ≅ ΔDCB ( by SAS congruency)
BD = CE (CPCT)
Hence, we have proved that medians bisecting the equal sides of an isosceles triangle are also equal.
We have to prove that BD = CE when AB = AC. ( where BD and CE are the medians)
In ∆ ABC
AB = AC ( Isosceles ∆)
∠B = ∠C…………..(1)
[ANGLE OPPOSITE TO EQUAL SIDES ARE EQUAL]
AB = AC
1/2 AB = 1/2 BC
BE = CD…………(2)
( as BD and CE are the medians of a triangle)
In ΔEBC & ΔDCB
∠B = ∠C ( From eq I)
BC = CB (Common)
BE= CD (From eq 2)
ΔEBC ≅ ΔDCB ( by SAS congruency)
BD = CE (CPCT)
Hence, we have proved that medians bisecting the equal sides of an isosceles triangle are also equal.
We have to prove that BD = CE when AB = AC. ( where BD and CE are the medians)
In ∆ ABC
AB = AC ( Isosceles ∆)
∠B = ∠C…………..(1)
[ANGLE OPPOSITE TO EQUAL SIDES ARE EQUAL]
AB = AC
1/2 AB = 1/2 BC
BE = CD…………(2)
( as BD and CE are the medians of a triangle)
In ΔEBC & ΔDCB
∠B = ∠C ( From eq I)
BC = CB (Common)
BE= CD (From eq 2)
ΔEBC ≅ ΔDCB ( by SAS congruency)
BD = CE (CPCT)
Hence, we have proved that medians bisecting the equal sides of an isosceles triangle are also equal.
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Hope this will help you..
Read more on Brainly.in - https://brainly.in/question/1666155#readmore
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Hope this will help you..
Read more on Brainly.in - https://brainly.in/question/1666155#readmore