# Using Triangle Similarity Theorems Assignment and Quiz

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 Is KM ∥ JN? Why or why not? D; Yes, because 16/10= 24/15 What is the length of ? GD = 10.5 Points S, U, and T are the midpoints of the sides of PQR. Which statements are correct? Check all that apply. 1/2QP = UT SU ∥ RP To prove part of the triangle midsegment theorem using the diagram, which statement must be shown? The length of GH is half the length of KL. What is the length of BC? From the markings on the diagram, we can tell E is the midpoint of BC and __ is the midpoint of AC We can apply the _____________________ theorem: ED = BA. Substituting in the expressions for the lengths and solving for x, we get x = __. Now, since BE = x, then BC = __ D triangle midsegment 5 10 What is the distance between points M and N? 9.8 Which value of x would make LK ∥ OM? x = 8 The diagram shows the intersections of several straight roads. The avenues run parallel to each other. Amana walks along Oak from point A to B. To the nearest foot, how far does she walk? 226 ft Given: STU with Prove: SX/XU = TY/YU Complete the steps of the proof. triangle STU is similar to triangle XYU subtraction property MO, MN, and ON are the midsegments of △JKL. What is the perimeter of △JKL? 19 If V is the midpoint of QS and W is the midpoint of RS, then what is VS? 20 units Using the side-splitter theorem, Daniel wrote a proportion for the segments formed by line segment DE. What is EC? 2.4 units Using the side-splitter theorem, which segment length would complete the proportion? GH/HE = ?/JF GJ What is the length of AJ if AB ∥ JK? 8.75 in Use the triangle midsegment theorem to solve for x. What is AX? 4 units Points O and N are midpoints of the sides of triangle DEF. What is DM? 38 cm Points J and K are midpoints of the sides of triangle FGH. What is the value of y? 7 Points A and B are midpoints of the sides of triangle QRS. What is SA? 4 m If CX = 5 units, then DZ = __ units. 4 Consider the paragraph proof. Given: D is the midpoint of AB, and E is the midpoint of AC. Prove:DE = BC It 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. Which is the missing information in the proof? a

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