Using Triangle Similarity Theorems Answers

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.

Consider the proof.Given: Segment AB is parallel to line DE. Prove:

Triangle X Y Z is cut by line segment C D. Line segment C D goes from side X Y to side Y Z. The length of C D is 15, the length of X Z is 18, the length of C Y is 25, and the length of Y D is 20. Lines C D and X Z are parallel.

Triangle R Q S is cut by line segment T U. Line segment T U goes from side Q R to side Q S. The length of Q T is 32, the length of T R is 36, the length of Q U is 40, and the length of U S is 45.

Triangle H J K is cut by line segment A B. Line segment A B goes from side H J to side H K. The length of H A is 5.25 inches, the length of H B is 3 inches, and the length of B K is 5 inches.

Triangle D E F is cut by line segment A B. Line segment A B goes from side D E to side F E. Lines D F and A B are parallel. The length of A B is 4.2 feet, the length of D A is 2 feet, the length of F B is 2.4 feet, and the length of B E is 7.8 feet.

Triangle A B C is cut by line segment D E. Line segment D E goes from side A B to B C. Lines A C and D E are parallel. The length of A D is 3, the length of D B is 5, the length of B E is 4, and the length of E C is question mark. StartFraction B D Over D A EndFraction = StartFraction B E Over E C EndFraction. StartFraction 5 Over 3 EndFraction = StartFraction 4 Over E C EndFraction

Points J and K are midpoints of the sides of triangle FGH.

Points A and B are midpoints of the sides of triangle QRS.

Triangle E G F is cut by line H J. Line H J goes from side E G through side G F. Lines E F and H J are parallel.