in ∆ABC, DE||BC, AD= 2cm, DB 3cm , DE:BC is equal to A. 2:3 B. 2:5 C. 1:2 D. 3:5
Answers
In ∆ABC, DE||BC, AD= 2cm, DB 3cm , DE:BC is equal to 2:5
Given:
- ΔABC
- DE || BC
- AD = 2 cm
- DB = 3 cm
To Find:
- DE:BC
Solution:
Corresponding angles : A pair of angles that occupy the same relative position at each intersection by a transversal line
Corresponding angles formed by transversal line with two parallel lines are
congruent. ( Equal in Measure)
Triangles with corresponding angles congruent are similar.
Corresponding sides of Similar Triangles are in proportion.
Step 1:
Compare ΔADE and ΔABC
∠A = ∠ A Common
∠D = ∠B (Corresponding angles)
∠E = ∠C (Corresponding angles)
ΔADE ~ ΔABC using AAA Similarity
Step 2:
Corresponding sides of Similar Triangles are in proportion.
DE/BC = AD/AB
Step 3:
Use AB = AD + DB and substitute AD = 2 and DB = 3
DE/BC = AD/(AD + DB)
=> DE/BC = 2/(2 + 3)
=> DE/BC = 2/5
=> DE : BC = 2 : 5
Correct option is B) 2 : 5
In ∆ABC, DE||BC, AD= 2cm, DB 3cm , DE:BC is equal to 2:5
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