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If a line is parallel to one side of a triangle, it divides the other two sides: A) Equally B) Perpendicularly C) Proportionally D) Unequally
C) Proportionally
In △ABC, if DE ∥ BC, then which of the following is true? A) AD = DB B) AE + EC = AD + DB C) AD/DB = AE/EC D) AD × DB = AE × EC
C) AD/DB = AE/EC
The Triangle Proportionality Theorem only applies when: A) The line passes through the midpoint of one side B) The line is parallel to one side C) The triangle is right-angled D) All sides are equal
B) The line is parallel to one side
If AD/DB = AE/EC, what can we conclude? A) DE ⟂ BC B) DE ∥ BC C) DE = BC D) Triangle ABC is isosceles
B) DE ∥ BC
The theorem helps prove which geometric property? A) Area of triangles B) Proportional sides C) Congruence of triangles D) Perimeter of polygons
B) Proportional sides
In a triangle, if a line divides the sides proportionally, it must be: A) Perpendicular to the base B) Parallel to the base C) Tangent to the base D) None of these
B) Parallel to the base
If DE ∥ BC, AD = 2, DB = 6, and AE = 3, find EC. A) 8 B) 9 C) 12 D) 7
B) 9
The Theorem is called the Basic Proportionality Theorem.
False- Triangle Proportionality Theorem
The converse of the theorem proves a line is parallel if the sides are divided proportionally.
True
The theorem works for any triangle shape (scalene, isosceles, or equilateral).
True
If a line is not parallel, the sides are always divided proportionally.
False- It has to be Parallel
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