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If two isosceles triangles have a common base, then the line joining their vertices will
- a)Bisect them at acute angle
- b)Bisect them at obtuse angle
- c)Bisect them at right angle
- d)NOT
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If two isosceles triangles have a common base, then the line joining t...
Given: ΔABC and ΔBCP are isosceles ΔS with common base BC.
In ΔS ABP and ACP
AB = AC (given)
BP = PC (given)
AP = AP (common)
∴ ΔABP ≅ ΔACP (S-S-S criterion)
∴ BO = OC and
∠AOB = ∠AOC = 180°
⇒ 2∠AOC = 180°
⇒ ∠AOB = 90°
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Community Answer
If two isosceles triangles have a common base, then the line joining t...
Explanation:
To understand why the line joining the vertices of two isosceles triangles with a common base bisects them at a right angle, let's consider the properties of isosceles triangles.
Properties of Isosceles Triangles:
1. In an isosceles triangle, the two sides opposite the equal angles are of equal length.
2. The angles opposite the equal sides of an isosceles triangle are equal.
Given:
We have two isosceles triangles with a common base.
To Prove:
The line joining their vertices bisects the triangles at a right angle.
Proof:
Let's label the triangles as ABC and ABD, where AB is the common base and AC = BC and AD = BD.
Now, let's draw the line joining the vertices C and D.
Step 1:
Since AC = BC and AD = BD, we can conclude that triangles ABC and ABD are congruent by the Side-Side-Side (SSS) congruence criterion.
Step 2:
Using the congruence of the triangles, we can say that angle BAC is congruent to angle BAD and angle ABC is congruent to angle ABD.
Step 3:
Since angles BAC and BAD are congruent, and angles ABC and ABD are congruent, we can conclude that angle CAB is congruent to angle DAB.
Step 4:
When two angles are congruent, they are called vertically opposite angles. Vertically opposite angles are always equal.
Step 5:
Since angle CAB and angle DAB are vertically opposite angles and congruent, we can conclude that the line joining the vertices C and D bisects the triangles ABC and ABD at a right angle.
Hence, the correct answer is option 'C' - The line joining the vertices of two isosceles triangles with a common base bisects them at a right angle.
To understand why the line joining the vertices of two isosceles triangles with a common base bisects them at a right angle, let's consider the properties of isosceles triangles.
Properties of Isosceles Triangles:
1. In an isosceles triangle, the two sides opposite the equal angles are of equal length.
2. The angles opposite the equal sides of an isosceles triangle are equal.
Given:
We have two isosceles triangles with a common base.
To Prove:
The line joining their vertices bisects the triangles at a right angle.
Proof:
Let's label the triangles as ABC and ABD, where AB is the common base and AC = BC and AD = BD.
Now, let's draw the line joining the vertices C and D.
Step 1:
Since AC = BC and AD = BD, we can conclude that triangles ABC and ABD are congruent by the Side-Side-Side (SSS) congruence criterion.
Step 2:
Using the congruence of the triangles, we can say that angle BAC is congruent to angle BAD and angle ABC is congruent to angle ABD.
Step 3:
Since angles BAC and BAD are congruent, and angles ABC and ABD are congruent, we can conclude that angle CAB is congruent to angle DAB.
Step 4:
When two angles are congruent, they are called vertically opposite angles. Vertically opposite angles are always equal.
Step 5:
Since angle CAB and angle DAB are vertically opposite angles and congruent, we can conclude that the line joining the vertices C and D bisects the triangles ABC and ABD at a right angle.
Hence, the correct answer is option 'C' - The line joining the vertices of two isosceles triangles with a common base bisects them at a right angle.
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If two isosceles triangles have a common base, then the line joining their vertices willa)Bisect them at acute angleb)Bisect them at obtuse anglec)Bisect them at right angled)NOTCorrect answer is option 'C'. Can you explain this answer?
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