Geometry Pre-test Quiz Plan for Similar Triangles 1

Geometry Pre–Test TRIANGLES 1.) State whether and SIMILAR are congruent. 7 [A] [B] [C] [D] (Questions 1 – 3 G.G.44) 7 yes, by either SSS or SAS yes, by SSS only yes, by SAS only No; there is not enough information to conclude that the triangles are congruent. 2.) Based on the given information, what can you conclude, and why? ∠ H ¿ ∠ L and HJ ¿ JL Given: I K J H Δ HIJ [A] AAS Δ HIJ [C] SAS L ¿ Δ LKJ by ASA [B] Δ HIJ ¿ Δ JLK by ¿ Δ JLK by SAS [D] Δ ¿ Δ LKJ by HIJ 3.) Name the theorem or postulate that lets you immediately conclude | A D | B C [A] SAS [B] ASA [C] AAS [D]none of these (Questions 4 – 6 G.G.45) 4.) A lamppost is 6 feet high and casts an 8-foot shadow. At the same time of day, a flagpole directly behind the lamppost casts a 28-foot shadow. Which proportion can be used to find the height, H, of the flagpole? H 6 28 = 8 [A] [B] H 8 6 28 = 8 28 [C] = H 6 H 28 [D] 8 6 = 5.) Two ladders are leaning against a wall at the same angle as shown. How far up the wall does the shorter ladder reach? [A] 8 ft [B] 10 ft [C] 6 ft [D] 20 ft 6.) Use similar triangles to find x. [A] 1.5 ft [B] 2.67 ft [C] 1.25 ft [D] 6 ft (Questions 7 – 9 G.G.46) 7.) Use the Side-Splitter Theorem to find x, given that . A 8 P 12 Q x 18 B C [A] 12 [B] 6 [C] 20 [D] 24 8.) Given , solve for x.The diagram is not drawn to scale. A x B 11 E 5 D [B] [A] 7 [C] C [D] 9.) In the figure shown, BC || DE , AB = 2 yards, BC = 9 yards, AE = 36 yards, and DE = 36 yards. Find BD. [A] 9 yd [B] 8 yd [C] 6 yd [D] 27 yd (Questions 10 – 12 G.G.47) 10.) The accompanying diagram shows part of the architectural plans for a structural support of a building. PLAN is a rectangle and AS ¿ LN. Which equation can be used to find the length of AS ? AS SN [A] [C] AS = LS [B] AS LS LS = SN [D] AN AS LN = LS LS AS AS = SN 11.) Use the diagram below to solve for a and for b. ) 8 10 6 a ) b [B] [A] [C] [D] 12.) Use the diagram below to solve for a and for b. ) 21 29 20 a ) b [A] [C] [B] [D] Name : ___________________________________________ Date : ___________________ A surveyor is given the task of measuring the distance across a lake from A to B. She set up he surveying equipment at point C and shoots in two lines to points E and D. She then records the following measurements. CA = 42 meters, CD = 70 meters, CB = 60 meters and CE = 100 meters. She found the length of DE to be 120 meters. How far across the lake is it? Explain the mathematics that you used to solve this problem. Is it alright to assume that triangle ABC and triangle CDE are similar? _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ A surveyor is given the Task of measuring the distance across a lake (AB). She decides to stake out the following similar triangles. Her surveying equipment allows her to determine that DC and FE are parallel. How does this information help her? _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ She can measure the distances: DC = 48 meters, FE = 72 meters, BC = 60 meters and FA = 40 meters, how is the surveyor going to use these measurements to help her find out the distance across the lake? _____________________________________________________ _____________________________________________________ _____________________________________________________ It is a bright sunny day and I decide I need to know the height of a large tree in my backyard that I want to have trimmed. I took my ladder out to measure the height of the tree but realized that it was not going to be tall enough to do the job. I was about to give up when my neighbor’s daughter who is studying high school geometry yelled over the fence that she could help me out. She measured the length of the tree’s shadow, which was 42 meters. Then she positioned the ladder, which is 2.4 meters high, and measured its shadow. The ladder’s shadow was exactly 3 meters. Where did she position the ladder and how did this model help her to find the length of the tree? Finally what was the tree’s length? __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ A surveyor is given the task of measuring the distance across a lake from A to B. She set up he surveying equipment at point C and shoots in two lines to points E and D. She then records the following measurements. CA = 44 meters, AD = 48 meters, CB = 55 meters. She found the length of DE to be 84 meters. In order for us to be able to easily solve this problem what must the distance be from B to E? Explain how we are able to use mathematics to help us with this situation. How far across the lake is it? __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ I need to measure the distance across the river. I am on one side and my co-worker is on the other side of the river. We want to place some stakes in the ground set up some triangles that will help us solve the problem. How do we set up our stakes and what measurements do we need to take? Make a problem up with the barest bit of information for your teacher to solve and find the distance across the river. __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ Name: ___________________ Date : ______________ Aim : To be able to use our knowledge of mid-segments to solve real world problems. Do Now In the figure below AC = 8cm. and AE = 16cm. Also B, is the midpoint of AD. What special name does BC have? If DE = 12 cm, what is the length of BC? Any mid-segment joins the midpoints of two adjacent sides of a triangle. This forms a segment which is parallel and half the length of the third side of the triangle. What knowledge of parallel lines and transversals can we use to prove that ∠ ABE is congruent to ADE? _____________________________________________________ ∠