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If one angle of triangle is equal to one angle of other triangle and the side including these angles are proportional, then two Triangles are similar .help plz do it as soon possible?
Most Upvoted Answer
If one angle of triangle is equal to one angle of other triangle and t...
Construction: Two triangles ABC and DEF are drawn so that one of the angles of one triangle is equal to one of the angles of another triangle. Moreover, two sides included in that angle of one triangle are proportional to two sides included in that angle of another triangle. This means;
∠ A = ∠ D and AB/DE=AC/DF
To Prove: Δ ABC ∼ Δ DEF
Draw PQ in triangle DEF so that, AB = DP and AC = DF
Proof:
ΔABC≅ΔDPQ ΔABC≅ΔDPQ
Because corresponding sides of these two triangles are equal
AB/DE=AC/DF...AB/DE=AC/DF given
∠ A = ∠ D
Hence; AB/DE=BC/...EF AB/DE=BC/EF from SSS criterion
Hence;
AB/DE=AC/DF=BC/EF..AB/DE=AC/DF=BC/EF
Hence; Δ ABC ∼ Δ DEF proved
I hope it's helpful for us...
∠ A = ∠ D and AB/DE=AC/DF
To Prove: Δ ABC ∼ Δ DEF
Draw PQ in triangle DEF so that, AB = DP and AC = DF
Proof:
ΔABC≅ΔDPQ ΔABC≅ΔDPQ
Because corresponding sides of these two triangles are equal
AB/DE=AC/DF...AB/DE=AC/DF given
∠ A = ∠ D
Hence; AB/DE=BC/...EF AB/DE=BC/EF from SSS criterion
Hence;
AB/DE=AC/DF=BC/EF..AB/DE=AC/DF=BC/EF
Hence; Δ ABC ∼ Δ DEF proved
I hope it's helpful for us...
Community Answer
If one angle of triangle is equal to one angle of other triangle and t...
Explanation:
Key Concepts:
- Angle-Angle (AA) similarity criterion
- Proportionality of sides in similar triangles
Angle-Angle (AA) Similarity Criterion:
When one angle of a triangle is equal to one angle of another triangle and the side including these angles are proportional, the triangles are similar by the Angle-Angle (AA) similarity criterion. This means that if two angles in one triangle are equal to two angles in another triangle, then the third angle in both triangles must also be equal, making the triangles similar.
Proportionality of Sides in Similar Triangles:
In similar triangles, the corresponding sides are in proportion. This means that the ratios of the lengths of the corresponding sides are equal. If the side including the equal angles in the two triangles are proportional, then all corresponding sides of the triangles will be proportional, leading to the triangles being similar.
Therefore, if one angle of a triangle is equal to one angle of another triangle and the side including these angles are proportional, then the triangles are similar according to the AA similarity criterion. This relationship allows us to determine the similarity of triangles based on their angle measures and side lengths.
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If one angle of triangle is equal to one angle of other triangle and the side including these angles are proportional, then two Triangles are similar .help plz do it as soon possible?
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If one angle of triangle is equal to one angle of other triangle and the side including these angles are proportional, then two Triangles are similar .help plz do it as soon possible? 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 If one angle of triangle is equal to one angle of other triangle and the side including these angles are proportional, then two Triangles are similar .help plz do it as soon possible? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one angle of triangle is equal to one angle of other triangle and the side including these angles are proportional, then two Triangles are similar .help plz do it as soon possible?.
If one angle of triangle is equal to one angle of other triangle and the side including these angles are proportional, then two Triangles are similar .help plz do it as soon possible? 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 If one angle of triangle is equal to one angle of other triangle and the side including these angles are proportional, then two Triangles are similar .help plz do it as soon possible? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one angle of triangle is equal to one angle of other triangle and the side including these angles are proportional, then two Triangles are similar .help plz do it as soon possible?.
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