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L and m are two Parallel lines intersected by another pair of Parallel lines p and Q (See fig. 7.19). Show that ∆ABC=~CDA?
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L and m are two Parallel lines intersected by another pair of Parallel...
Understanding the Configuration
In the given scenario, we have two pairs of parallel lines: lines L and M are parallel, and lines P and Q are also parallel. The intersection of these lines forms two triangles, ∆ABC and ∆CDA.
Identifying the Triangles
- Triangle ∆ABC is formed by vertices A, B, and C.
- Triangle ∆CDA is formed by vertices C, D, and A.
Properties of Parallel Lines
- When a transversal intersects two parallel lines, corresponding angles are equal.
- Therefore, the angles formed at the intersection points can be analyzed.
Establishing Angle Relationships
- Angle ACB (in ∆ABC) is equal to Angle DCA (in ∆CDA) because they are corresponding angles created by the transversal line P intersecting the parallel lines L and M.
- Angle ABC (in ∆ABC) is equal to Angle CDA (in ∆CDA) for the same reason.
Common Side
- Both triangles share a common side, AC.
Applying the Angle-Angle (AA) Criterion
- Since we have two pairs of equal angles (Angle ACB = Angle DCA and Angle ABC = Angle CDA), we can use the Angle-Angle (AA) similarity criterion.
- The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
Conclusion
- Therefore, we conclude that ∆ABC is similar to ∆CDA, denoted as ∆ABC = ~CDA.
- This similarity indicates that the triangles have the same shape but may differ in size.
In the given scenario, we have two pairs of parallel lines: lines L and M are parallel, and lines P and Q are also parallel. The intersection of these lines forms two triangles, ∆ABC and ∆CDA.
Identifying the Triangles
- Triangle ∆ABC is formed by vertices A, B, and C.
- Triangle ∆CDA is formed by vertices C, D, and A.
Properties of Parallel Lines
- When a transversal intersects two parallel lines, corresponding angles are equal.
- Therefore, the angles formed at the intersection points can be analyzed.
Establishing Angle Relationships
- Angle ACB (in ∆ABC) is equal to Angle DCA (in ∆CDA) because they are corresponding angles created by the transversal line P intersecting the parallel lines L and M.
- Angle ABC (in ∆ABC) is equal to Angle CDA (in ∆CDA) for the same reason.
Common Side
- Both triangles share a common side, AC.
Applying the Angle-Angle (AA) Criterion
- Since we have two pairs of equal angles (Angle ACB = Angle DCA and Angle ABC = Angle CDA), we can use the Angle-Angle (AA) similarity criterion.
- The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
Conclusion
- Therefore, we conclude that ∆ABC is similar to ∆CDA, denoted as ∆ABC = ~CDA.
- This similarity indicates that the triangles have the same shape but may differ in size.
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L and m are two Parallel lines intersected by another pair of Parallel lines p and Q (See fig. 7.19). Show that ∆ABC=~CDA?
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L and m are two Parallel lines intersected by another pair of Parallel lines p and Q (See fig. 7.19). Show that ∆ABC=~CDA? 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 L and m are two Parallel lines intersected by another pair of Parallel lines p and Q (See fig. 7.19). Show that ∆ABC=~CDA? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for L and m are two Parallel lines intersected by another pair of Parallel lines p and Q (See fig. 7.19). Show that ∆ABC=~CDA?.
L and m are two Parallel lines intersected by another pair of Parallel lines p and Q (See fig. 7.19). Show that ∆ABC=~CDA? 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 L and m are two Parallel lines intersected by another pair of Parallel lines p and Q (See fig. 7.19). Show that ∆ABC=~CDA? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for L and m are two Parallel lines intersected by another pair of Parallel lines p and Q (See fig. 7.19). Show that ∆ABC=~CDA?.
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