Using Triangle Similarity Theorems Answers

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Consider the paragraph proof.Given: D is the midpoint of AB, and E is the midpoint of AC.Prove:DE = BCIt is given that D is the midpoint of AB and E is the midpoint of AC. To prove that DE is half the length of BC, the distance formula, d = , can be used to determine the lengths of the two segments. The length of BC can be determined with the equation BC = , which simplifies to 2a. The length of DE can be determined with the equation DE = , which simplifies to ________. Therefore, BC is twice DE, and DE is half BC.

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A
a
B
4a
C
a2
D
4a2
2
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Points S and T are midpoints of the sides of triangle FGH.

Question illustration
A
4 cm
B
6 cm
C
8 cm
D
16 cm
4

Which statements about triangle JKL are true? Select two options.

A
M is the midpoint of line segment KJ.
B
N is the midpoint of line segment JL.
C
MN = KJ
Option C
D
MN = 4.4m
E
MN = ML
8

Which statements are true? Select three options. (The formula for the area of a triangle is A = bh.)

Question illustration
A
BC = 6 cm
B
AC = 5 cm
C
BA = 4 cm
D
The perimeter of triangle ABC = 12 cm.
E
The area of triangle ABC is the area of triangle DEF.
Option E
10

Triangle A B C is cut by line segment D E. Line segment D E goes from side A C to line A B. The length of A E is 12, the length of E B is 4, and the length of A D is 9.

Question illustration
A
2 units
B
3 units
C
6 units
D
9 units

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