Lesson 7.1_ Similar Polygons_ Attempt review _ VSC.pdf

Started on Tuesday, January 30, 2024, 5:32 PM State Finished Completed on Tuesday, January 30, 2024, 5:36 PM Time taken 4 mins 20 secs Points 27.00/28.00 Grade 96.43 out of 100.00 Information Information Review of Ratios What if you wanted to make a scale drawing of your room and furniture for a little redecorating? Your room measures feet by feet. Also in your room is a twin bed ( in by in), a desk ( feet by feet), and a chair ( feet by feet). You decide to scale down your room to in by in, so the drawing fits on a piece of paper. What size should the bed, desk and chair be? Draw an appropriate layout for the furniture within the room. Do not round your answers. By the end of this section you will be able to perform this task. Writing Ratios A ratio is a way to compare two numbers. Ratios can be written: , , and to . Let's look at some examples. Problem There are girls and boys in your math class. What is the ratio of girls to boys? Remember that order matters. Solution The question asked for the ratio of girls to boys. The ratio would be . This can be simplified to .

Information Information Information Simplifying Ratios: Example 1 Problem Simplify the following ratio: \(\frac{7\;ft.}{14\;in.}\). Solution First, change each ratio so that each part is in the same units. Remember, there are 12 inches in a foot. \(\frac{7\;ft.}{14\;in.}\cdot\frac{12\;in.}{1\;ft.}=\frac{84}{14}=\frac61\) The inches and feet cancel each other out. Simplified ratios do not have have units. Example 2 Problem Simplify the following ratio: \(9m:900cm\) Solution It is easier to simplify a ratio when written as a fraction. \(\frac{9\;m}{900\;cm}\cdot\frac{100\;cm}{1\;m}=\frac{900}{900}=\frac11\) Example 3 Problem Simplify the following ratio: \(\frac{4\;gal.}{16\;gal.}\) Solution \(\frac{4\;gal.}{16\;gal.}=\frac14\)

Information Information Information Example 4 Problem A talent show has dancers and singers. The ratio of dancers to singers is \(3:2\). There are \(30\) performers total, how many of each are there? Solution To solve, notice that \(3:2\) is a reduced ratio, so there is a number, \(n\), that we can multiply both by to find the total number in each group. Represent dancers and singers as expressions in terms of \(n\). Then set up and solve an equation. dancers \(=3n\) singers \(=2n\) \(3n+2n=30\) \(5n=30\) \(n=6\) There are \(3\cdot6=18\) dancers and \(2\cdot6=12\) singers. Example 5: Video Let’s watch a quick video on ratios. Video: What's a ratio? (opens in a new window) Guided Practice You will have 3 attempts for each problem below. A correct answer on the first attempt earns full credit. A correct answer on the second or third attempt will earn partial credit. A hint will be given after the first incorrect answer. Remember, you can redo the entire lesson once you have figured out what you are struggling on, even if you have used all attempts on a question. Your highest grade for the overall lesson will be recorded and you must make an 80, or above, in order to move on to the next lesson.

Question 1 Correct 9.00 points out of 9.00 Question 2 Correct 2.00 points out of 2.00 Information Problem 1 The votes for president in a club election were: Smith: \(24\) Munoz: \(32\) Park: \(20\) Find the following ratios and write in simplest form . Votes for Munoz to Smith 4 \(:\) 3 Votes for Park to Munoz 5 \(:\) 8 Votes for Smith to total votes 6 \(:\) 19 Votes for Smith to Munoz to Park 6 \(:\) 8 \(:\) 5 Problem 2 The length and width of a rectangle are in a \(3:5\) ratio. The perimeter of the rectangle is \(64\). What are the length and width of the rectangle? The length is 12 and the width is 20 . Problem Revisited Remember the situation where you needed to scale down your room to fit on a sheet of paper so that you could experiment with where your furniture could go? Everything needs to be scaled down by a factor of \(\frac{1}{18}\) (\(144\;in.\div\;8\;in\)). Change everything into inches and then multiply by the scale factor. Bed: \(36\) in. by \(75\) in. \(\rightarrow\) \(2\) in. by \(4.167\) in. Desk: \(48\) in. by \(24\) in. \(\rightarrow\) \(2.67\) in. by \(1.33\) in. Chair: \(36\) in. by \(36\) in. \(\rightarrow\) \(2\) in. by \(2\) in. There are several layout options for these three pieces of furniture. Draw an \(8\) in. by \(8\) in. square and then the appropriate rectangles for the furniture. Then, cut out the rectangles and place inside the square.

Information Information Information Review of Proportions What if you were told that a scale model of a python is in the ratio of \(1:24\)? If the model measures \ (0.75\) feet long, how long is the real python? We will discuss the answer at the end of this section. Proportions A proportion is when two ratios are set equal to each other. Cross-Multiplication Theorem: Let \(a\), \(b\), and \(c\), and \(d\) be real numbers, with \(b\neq0\) and \(d\neq0\). If \(\frac ab=\frac cd\), then \(ad=bc\). The proof of the Cross-Multiplication Theorem is an algebraic proof. Recall that multiplying by \(\frac22\), \(\frac bb\), or \(\frac dd=1\) because it is the same number divided by itself (\(b\div b=1\)). Solving Proportions: Example 1 Problem Solve for x. \(\frac45=\frac{x}{30}\) Solution To solve a proportion, you need to cross-multiply. \(\frac45=\frac{x}{30}\) \(4\cdot30=5\cdot x\) \(120=5x\) \(24=x\)

Information Information Solving Proportions: Example 2 Problem Solve for y. \(\frac{y+1}{8}=\frac{5}{20}\) Solution To solve a proportion, you need to cross-multiply. \(\frac{y+1}{8}=\frac{5}{20}\) \((y+1)\cdot20=5\cdot8\) \(20y+20=40\) \(20y=20\) \(y=1\) Solving Proportions: Example 3 Problem Solve for x. \(\frac65=\frac{2x+4}{x-2}\) Solution To solve a proportion, you need to cross-multiply. \(\frac65=\frac{2x+4}{x-2}\) \(6\cdot(x-2)=5\cdot(2x+4)\) \(6x-12=10x+20\) \(-32=4x\) \(-8=x\)

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help