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Let’s grade homework Pg 138 – 143; 5-9, 17-21, not 8c 3.1.3 - Proportional Equations 3.1.4 – Using Proportional equations Ratio Proportion A comparison of 2 things. An equation where 2 ratios are equal to each other Can be written like: Written like: Dogs : cats (in words) 2:1 (with a colon) (3 + x) = 5 7 2 3 4 (as a fraction) Use cross products to solve. How are ratios and proportions the same? How are they different? I will number each row. Back person: please get the appropriate paper from the back table – one paper for each person – and hand them out. Second person from the back: please get a straightedge for everyone in your row. Everyone: please follow the instructions on the paper and complete your paper independently. In 5 minutes, you will be able to compare your answers to others in your row to come up with a final solution. Then, make a table and come up with some conjectures.. • • • • • • • #1 Put a point of dilation somewhere inside the shape. Measure the sides of your shape in cm. Dilate the shape by a scale factor of 2. Find the perimeter of the pre-image. Find the perimeter of the image. Find the area of the pre-image. Find the area of the image. #2 #4 #3 #5 shape 1 perimeter of pre-image perimeter of image area of pre-image area of image shape 2 shape 3 shape 4 shape 5 Naming & Comparing Polygons ♥ List vertices in order, either clockwise or counterclockwise. ♥ When comparing 2 polygons, begin at corresponding vertices; name the vertices in order and; go in the same direction. ♥ By doing this you can identify corresponding parts. D E C A B DCBAE I H J P D corresponds to I AE corresponds to PH K IJKPH Name corresponding parts • Name all the angles that correspond: I D corresponds to I C corresponds to J E B corresponds to K A corresponds to P A E corresponds to H D H C J B P DCBAE IJKPH K • Name all the segments that correspond: DC corresponds to IJ CB corresponds to JK BA corresponds to KP AE corresponds to PH ED corresponds to HI How many corresponding angles are there? 5 How many corresponding sides are there? 5 D E C A • How many ways can you name pentagon DCBAE? 10 B Do it. Pick a vertex and go clockwise Pick a vertex and go counterclockwise DCBAE DEABC CBAED CDEAB BAEDC BCDEA AEDCB ABCDE EDCBA EABCD Similarity Statements • Given: These polygons are similar. A E B F • Remember, if they are SIMILAR, corresponding sides have the same RATIO. D C AB ~ EF H DA ~ HE DC ~ HG CB ~ GF G ABCD ~ EFGH Corresponding angles in a similar figure are congruent!! Corresponding angles in a similar figure are congruent A E B D C H G F A ~= E B ~= F D ~= H C ~= G Quick check How many different ways can you name ΔABC? What is the relationship of corresponding sides in a similar figure? What is the relationship of corresponding angles in a similar figure? What happens to the perimeter of a shape that has been dilated by a scale factor of 2? What happens to the area of a shape that has been dilated by a scale factor of 2? What is the simplified, exact answer to: √3 + 5√3 ? What is the name of angle pair c and h? Are angles c and h congruent, supplementary or neither? Defend your answer. What is the name of angle pair b and g? What is the measurement relationship between b and g? Defend your answer. What is the sum of the angles in a triangle? What is the sum of the angles in a quadrilateral? If a shape has a scale factor of 3, is the pre-image larger or smaller than the image? e a b f c h d g Your assignment Pg 146 – 151; 27-31, 38-42