Question Video: Identifying the Equal Proportions between Corresponding Sides in Two Similar Triangles | Nagwa Question Video: Identifying the Equal Proportions between Corresponding Sides in Two Similar Triangles | Nagwa

# Question Video: Identifying the Equal Proportions between Corresponding Sides in Two Similar Triangles Mathematics • First Year of Secondary School

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Using the diagram, which of the following is equal to π΄π΅/π΄π·? [A] π΄π΅/π·π΅ [B] π΄πΆ/π΄πΈ [C] π΄πΆ/πΈπΆ [D] π΄π·/π·π΅ [E] π΄πΈ/πΈπΆ

02:16

### Video Transcript

Using the diagram, which of the following is equal to π΄π΅ over π΄π·. Is it (A) π΄πΆ over πΈπΆ or (B) π΄π΅ over π·π΅ or (C) π΄π· over π·π΅, answer (D), π΄πΆ over π΄πΈ, or (E) π΄πΈ over πΈπΆ.

We see from the diagram that the base of triangle π΄πΈπ·, thatβ²s side πΈπ·, is parallel to the base of triangle π΄π΅πΆ, thatβ²s side πΆπ΅. Since corresponding angles must be equal if the two lines are parallel, angle π·πΈπ΄ is equal to angle π΅πΆπ΄, and angle πΈπ·π΄ is equal to angle πΆπ΅π΄. Then side πΈπ· creates triangle π΄π·πΈ, which is similar to the larger triangle π΄π΅πΆ. Since these triangles are similar, the ratios of their corresponding side lengths must be equal. In particular, π΄πΈ over π΄πΆ is equal to π΄π· over π΄π΅.

Now we want to find which of the given fractions is equal to π΄π΅ over π΄π·. And we can do this by finding the reciprocal of both sides of our equation, which gives us π΄πΆ over π΄πΈ is equal to π΄π΅ over π΄π·. Hence, π΄π΅ over π΄π· is equal to π΄πΆ over π΄πΈ, which corresponds to the given option (D).

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