Podcast
Questions and Answers
In triangle ABC, if altitudes BE and CF are equal, then triangle ABE and triangle ACF are congruent.
In triangle ABC, if altitudes BE and CF are equal, then triangle ABE and triangle ACF are congruent.
True (A)
What congruence criterion is used to prove that ΔABE = ΔACF?
What congruence criterion is used to prove that ΔABE = ΔACF?
If the altitudes BE and CF are equal in triangle ABC, what can you conclude about the sides AB and AC?
If the altitudes BE and CF are equal in triangle ABC, what can you conclude about the sides AB and AC?
AB = AC
A triangle with two equal sides is called an ______ triangle.
A triangle with two equal sides is called an ______ triangle.
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Match the following terms with their definitions:
Match the following terms with their definitions:
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Study Notes
Given Information
- Triangle ABC has altitudes BE and CF drawn to sides AC and AB, respectively.
- The altitudes BE and CF are equal in length.
Proof of ΔABE ≅ ΔACF (i)
- Consider triangles ABE and ACF.
- ∠AEB = ∠AFC = 90° (Since BE and CF are altitudes)
- ∠A is common to both triangles.
- BE = CF (Given)
- Therefore, ΔABE and ΔACF are congruent by the right angle-hypotenuse-side (RHS) congruence criterion.
Proof of AB = AC (ii)
- Since ΔABE ≅ ΔACF, corresponding sides are equal.
- Thus, AB = AC.
Conclusion
- AB = AC implies that triangle ABC is an isosceles triangle.
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Description
This quiz explores the properties of isosceles triangles through congruence proofs. You will analyze the congruence of triangles ABE and ACF given specific altitudes are equal. Test your understanding of triangle properties and congruence criteria.
