How can I prove that the base angles of an isosceles triangle are equal?
An example of an AI chatbot conversation about proving base angles in isosceles triangles.
How can I prove that the base angles of an isosceles triangle are equal?
To prove that the base angles of an isosceles triangle are equal, you can use the properties of congruent triangles.
What properties of congruent triangles should I use?
You can use the Side-Angle-Side (SAS) postulate. If two sides are equal, the angles opposite those sides are also equal.
Can you give me a step-by-step proof?
Sure! 1. Let triangle ABC be isosceles with AB = AC. 2. Draw a line segment from A to the midpoint D of BC. 3. Now, triangles ABD and ACD are congruent by SAS. 4. Therefore, angle ABD = angle ACD.
What if I want to prove it using a different method?
You could also use the concept of exterior angles. The exterior angle is equal to the sum of the two opposite interior angles.
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