To complete: The given statements
Answer to Problem 2CE
Explanation of Solution
According to Basic proportionality theorem, if a line intersects two sides at distinct points and parallel to the third side then the other two sides are divided in the same proportion.
As
Now prove
Now
(Each pair of alternate interior angles are equal when a transversal intersects two parallel lines)
Also,
(Each pair of alternate interior angles are equal when a transversal intersects two parallel lines)
Therefore,
(according to AA similarity criteria, if two angles of one triangle are equal to the two angles of another triangle then the triangles are similar)
So,
(If two triangles are similar then the following conditions are satisfied:
1. Corresponding sides of the polygons are proportional.
2. Corresponding angles of the polygons are equal.)
In the given figure,
Lower left is BD
Lower right is BD
Whole left is AB
Whole right is AC
Upper left is AD
Upper right is AE
Upper parallel is DE
Lower parallel is BC
From (i),
From (ii),
From (iii),
Chapter 7 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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