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In triangle ABC D abd E are midpoint of side BC and AC respectively. Find length of DE . Prove that DE =1/2 AB?
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In triangle ABC D abd E are midpoint of side BC and AC respectively. F...
First Find the points D and E by midpoint formula.
(x₂+x₁/2, y₂+y₁/2)
For DE=1/2AB
In ΔsCED and CAB
∠ECD=∠ACB
and the ratio of the side containing the angle is the same i.e,
CD=1/2BC
⇒CD/BC=1/2
EC=1/2AC
⇒EC/AC=1/2
∴, ΔCED~ΔCAB
hence the ratio of their corresponding sides will be equal,
DE=1/2AB
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In triangle ABC D abd E are midpoint of side BC and AC respectively. F...
Understanding Triangle ABC
In triangle ABC, let D and E be the midpoints of sides BC and AC, respectively. We want to find the length of segment DE and prove that DE = 1/2 AB.
Using the Midpoint Theorem
- The Midpoint Theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
- Here, DE connects midpoints D (of BC) and E (of AC).
Applying the Theorem
- Since DE connects the midpoints of sides BC and AC:
- DE is parallel to side AB.
- The length of DE is half the length of AB.
Proof of Length
1. Identify Midpoints:
- D is the midpoint of BC.
- E is the midpoint of AC.
2. Parallelism:
- DE || AB (by Midpoint Theorem).
3. Length Calculation:
- Length of DE = 1/2 the length of AB.
- Hence, DE = 1/2 AB.
Conclusion
In triangle ABC, by applying the Midpoint Theorem, we have established that the segment DE, connecting the midpoints D and E, is equal to 1/2 the length of side AB. This relationship is fundamental in understanding the properties of triangles and their segments.
In triangle ABC, let D and E be the midpoints of sides BC and AC, respectively. We want to find the length of segment DE and prove that DE = 1/2 AB.
Using the Midpoint Theorem
- The Midpoint Theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
- Here, DE connects midpoints D (of BC) and E (of AC).
Applying the Theorem
- Since DE connects the midpoints of sides BC and AC:
- DE is parallel to side AB.
- The length of DE is half the length of AB.
Proof of Length
1. Identify Midpoints:
- D is the midpoint of BC.
- E is the midpoint of AC.
2. Parallelism:
- DE || AB (by Midpoint Theorem).
3. Length Calculation:
- Length of DE = 1/2 the length of AB.
- Hence, DE = 1/2 AB.
Conclusion
In triangle ABC, by applying the Midpoint Theorem, we have established that the segment DE, connecting the midpoints D and E, is equal to 1/2 the length of side AB. This relationship is fundamental in understanding the properties of triangles and their segments.
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In triangle ABC D abd E are midpoint of side BC and AC respectively. Find length of DE . Prove that DE =1/2 AB?
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In triangle ABC D abd E are midpoint of side BC and AC respectively. Find length of DE . Prove that DE =1/2 AB? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In triangle ABC D abd E are midpoint of side BC and AC respectively. Find length of DE . Prove that DE =1/2 AB? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In triangle ABC D abd E are midpoint of side BC and AC respectively. Find length of DE . Prove that DE =1/2 AB?.
In triangle ABC D abd E are midpoint of side BC and AC respectively. Find length of DE . Prove that DE =1/2 AB? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In triangle ABC D abd E are midpoint of side BC and AC respectively. Find length of DE . Prove that DE =1/2 AB? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In triangle ABC D abd E are midpoint of side BC and AC respectively. Find length of DE . Prove that DE =1/2 AB?.
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