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If D is a point on the side AB of triangle ABC and DE is a line through D meeting AC at E such that ∠ADE = ∠ACB, then AB. AD is equal to:
- a)AE.BC
- b)AC.DE
- c)AE.AC
- d)AB.BC
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If D is a point on the side AB of triangle ABC and DE is a line throu...
Clearly ΔADE and ΔABC are similar
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∴ AD/AC = AE/AB
AD. AB = AE. AC
Most Upvoted Answer
If D is a point on the side AB of triangle ABC and DE is a line throu...
To solve this question, we can use the angle bisector theorem and the similarity of triangles. Here's the step-by-step solution:
1. Let's draw a diagram of triangle ABC with point D on side AB and line DE passing through D and intersecting side AC at point E.
2. Since ∠ADE = ∠ACB, we can conclude that triangles ADE and ACB are similar by the Angle-Angle Similarity Postulate.
3. By the angle bisector theorem, we know that the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the lengths of the sides opposite those segments.
4. Applying the angle bisector theorem in triangle ABC, we have:
AD / DB = AC / CB
5. Now, using the similarity of triangles ADE and ACB, we can write:
AD / AE = AC / AB
6. Rearranging the above equation, we get:
AB / AD = AC / AE
7. From the given options, we can see that option 'C' matches the above equation:
AB / AD = AE / AC
8. Therefore, option 'C' is the correct answer.
In conclusion, according to the angle bisector theorem and the similarity of triangles, we can determine that AB / AD is equal to AE / AC.
1. Let's draw a diagram of triangle ABC with point D on side AB and line DE passing through D and intersecting side AC at point E.
2. Since ∠ADE = ∠ACB, we can conclude that triangles ADE and ACB are similar by the Angle-Angle Similarity Postulate.
3. By the angle bisector theorem, we know that the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the lengths of the sides opposite those segments.
4. Applying the angle bisector theorem in triangle ABC, we have:
AD / DB = AC / CB
5. Now, using the similarity of triangles ADE and ACB, we can write:
AD / AE = AC / AB
6. Rearranging the above equation, we get:
AB / AD = AC / AE
7. From the given options, we can see that option 'C' matches the above equation:
AB / AD = AE / AC
8. Therefore, option 'C' is the correct answer.
In conclusion, according to the angle bisector theorem and the similarity of triangles, we can determine that AB / AD is equal to AE / AC.
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If D is a point on the side AB of triangle ABC and DE is a line through D meeting AC at E such that ∠ADE = ∠ACB, then AB. AD is equal to:a)AE.BCb)AC.DEc)AE.ACd)AB.BCCorrect answer is option 'C'. Can you explain this answer?
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