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Line segment AB is paralleled to another line segment CD. O is the mid point of AD. Show that
triangle AOB congruent to Triangle DOC.
O is the mid point of BC.
Verified Answer
Line segment AB is paralleled to another line segment CD. O is the mid...
Given: AB = CD ; O is the mid - point .
To proof : ABC is congruent to DOC
Proof : IN triangle AOB and DOC ,
AB = CD ( given )
<OAB = <ODC ( alternate interior angles )
<AOB = <DOC ( vertically opposite angles )
Therefore , triangle AOB is congruent to DOC (ASA rule )
OB = OC ( C.PC.CT)
Hence , O is also the mid point of BC
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
Line segment AB is paralleled to another line segment CD. O is the mid...
Proof of Triangle Congruence: AOB ≅ DOC
1. Given Information:
- Line segment AB is parallel to line segment CD.
- O is the midpoint of segment AD.
- O is the midpoint of segment BC.
2. Reasoning:
- Since AB is parallel to CD, angle AOB is equal to angle DOC as corresponding angles.
- Triangle AOB and triangle DOC share a common side AO and DO.
- Also, O is the midpoint of both AD and BC, which implies that AO = OD and BO = OC.
3. Proof of Triangle Congruence:
- By Side-Angle-Side postulate, we have AO = OD (common side), angle AOB = angle DOC (corresponding angles), and BO = OC (midpoint property).
- Therefore, triangle AOB is congruent to triangle DOC by SAS congruence.
4. Conclusion:
- Triangle AOB is congruent to triangle DOC based on the given information and the properties of midpoints and parallel lines.
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Line segment AB is paralleled to another line segment CD. O is the mid point of AD. Show that
triangle AOB congruent to Triangle DOC.
O is the mid point of BC.
Question Description
Line segment AB is paralleled to another line segment CD. O is the mid point of AD. Show that triangle AOB congruent to Triangle DOC. O is the mid point of BC. for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Line segment AB is paralleled to another line segment CD. O is the mid point of AD. Show that triangle AOB congruent to Triangle DOC. O is the mid point of BC. covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Line segment AB is paralleled to another line segment CD. O is the mid point of AD. Show that triangle AOB congruent to Triangle DOC. O is the mid point of BC. .
Line segment AB is paralleled to another line segment CD. O is the mid point of AD. Show that triangle AOB congruent to Triangle DOC. O is the mid point of BC. for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Line segment AB is paralleled to another line segment CD. O is the mid point of AD. Show that triangle AOB congruent to Triangle DOC. O is the mid point of BC. covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Line segment AB is paralleled to another line segment CD. O is the mid point of AD. Show that triangle AOB congruent to Triangle DOC. O is the mid point of BC. .
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O is the mid point of BC.
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