I can use ratio, rate and proportion to investigate similar triangles and solve problems.

Transcription

1 MFM2P Similar Triangles Checklist 1 Goals for this unit: I can use ratio, rate and proportion to investigate similar triangles and solve problems. U1L1: Geometric Concepts Learning Goal: Review geometric topics and solve ratios U1L2: Similar Triangles Learning Goal: I can use ratios to determine unknowns in similar triangles. U1L3: Solving Problems using Similar Triangles Learning Goal: I can solve real - world problems involving similar triangles. Review Note Assigned Work Page #5, 3-5 Journal One Note Assigned Work Page 25, #1, 3-6, 8-10 Journal Two Note Assigned Work Page 33, # 1, 2, 4-12 Journal Three Assigned Work Page 39 #10-16 Page 40 #8-12

2 MFM2P U1L1 Review of Geometric Concepts Today's Topic : Review of skills Today's Goal : Review geometric topics and solve ratios Review of Geometry Concepts o x x o T x y z y x z

3 MFM2P U1L1 Review of Geometric Concepts Whenever a pair of parallel lines is cut by a transversal... a) c b) a c) i

4 MFM2P U1L1 Review of Geometric Concepts Solving Proportions Solve the following ratio in three different ways By Comparison Find the multiplication factor from one ratio to the other, or between numerator and denominator and use it to either multiply/divide to find the missing value. By Isolation Get the variable to the top of the ratio (if it isn't already) by flipping BOTH ratios. Multiply both ratios by the number under the variable. Do the math! By Cross Multiplication Multiply each numerator by the opposite denominator and set the products equal. Divide both sides by the coefficient of the variable to solve. MFM 2P Homework Page 4 #1 5

5 MFM 2P U1L2 Similar Triangles Today's Topic : Today's Goal : Similar Triangles To understand the properties of similar triangles and use them to find lengths of missing sides in pairs of similar triangles. 6.2 Similar Triangles When two objects are the same size and the same shape they are called congruent. When two objects are the same shape, but different sizes, they are said to be similar. We are going to look at similar triangles. What makes triangles the same shape is the fact that they have all angles equal. Q A R S B C We name vertices of triangles with capital letters, and the side opposite them is labeled with the same lower case letter.

6 MFM 2P U1L2 Similar Triangles Remember when naming similar triangles, the order of the letters are important. They must go in the same order, by equal angles. Example 1. If ABC~ QRS, mark the equal angles, and set up ratios to find the missing sides a 8 5 r

7 MFM 2P U1L2 Similar Triangles Example 2. If ST is parallel to QR, set up ratios to find the missing values. MPM 2D Homework Page 322 #1 3, 5, 6 MFM 2P Homework Page 25 #1 3, 5, 10

8 MFM 2P U1L3 Problems with Similar Triangles Today's Topic: similar triangles Today's Goal : to use similar triangles to measure distances or objects that may otherwise be difficult to measure. Problems with Similar Triangles Example 1. Measuring Zac Zac is so tall we can't just can't measure him with a measuring tape. So Chad who knows that his eye is cm above the floor positions a mirror exactly 2 m from Zac 's feet. Then he walks backwards until Zac's head is visible in the centre of the mirror. Chad is now m from the mirror. How tall is Zac? Example 2. To determine how tall a statue is, a mirror is placed on the ground then you move away from the mirror until you can just see the top of the statue in the mirror. The following diagram represents this situation. What is the height of the statue?

9 MFM 2P U1L3 Problems with Similar Triangles Did you know, that any shadow cast by the sun at any given moment will form a similar triangle with any other shadow at that given moment? Example 3. A 1 metre stick is placed in the ground in order to determine the height of a tree. The shadow of the tree is measured at 8.7 m. The shadow of the metre stick is 1.6 metres. What is the height of the tree. Example 4. To measure the distance across a lake the following triangles are set up and the measurements taken. What is the distance across the lake? MPM 2D : Homework Page 324 #5-10, 15 & MM MFM 2P : Homework Page 33 #4-10, 12