Honors Geometry 25/26 Jan 2012 WARM UP- THINK- 3 minutes silently PAIR- chat with a partner 1. ABCD is a parallelogram. What is the measure of angle D? a) 22.5⁰ b) 45 c) 67.5⁰d) 112.5⁰ 2. Find x and check your answer: x (x – 2) = 3x + 6 What do the values of x represent on the graph? (5x) ⁰ (3x) ⁰ A B C D

objective Students will calculate the ratio of the circumference of a circle to its diameter and use it to solve problems. Homework due FRIDAY pg. 337+: 1 – 12, 21, 22

Project See handout PROJECT DUE: FEBRUARY 6

practice 1) x x ) x x ) x 2 + 3x -28 4) x 2 -12x -28 MULTIPLY- use FOIL or box 5) (2x + 3)(4x – 5) 6) (5x + 4)(5x – 6)

using factoring to solve equations Find x if x 2 + 5x + 6 = 0 a) find the factors of the quadratic b) set EACH factor equal to ZERO and solve c) check (x + 2)(x + 3) = 0 so x + 2 = 0 OR x + 3 = 0 either would make the equation true x = -2 OR x = - 3 (-2) 2 + 5(-2) + 6 = = 0 0 = 0√ (-3) 2 + 5(-3) + 6 = = 0 0 = 0√

pg. 441: ) rearrange equation through balancing to end up with …. = 0 2) factor the quadratic 3) set each factor = 0 and solve 4) check your answers GRAPH your equation– what do you notice? 0= graph as Y=

summary A parallelogram = bh A triangle = ½ bh A trapezoid =½ (b 1 +b 2 )h A kite = ½ (d 1 )(d 2 ) A regular polygon = ½ san

what do you think? which is greater, the height of a tennis ball can or the circumference of the can? explain your thinking…

words to know perimeter the distance around a polygon circumference the distance around a circle diameter a segment with endpoints on the circle that includes the center of the circle radius a line segment from the center of a circle to a point on the circle irrational number a number that when in decimal form, never ends or repeats

Investigation, pg. 336 Read steps 1 – 4 silently to yourself. Summarize each step in writing on your paper. Your write up is to be submitted for class work. Work with your group to complete the investigation. SUPPLIES- measuring tapes, 4 different sized round objects, calculator Also, each group needs to write your table from step 2 on a white board to share with the class.

Circumference Conjecture If C is the circumference and d is the diameter of a circle, then there is a number π such that π = C /d or by multiplying both sides by d, C = πd If d = 2r where r is the radius, then C = 2πr.

debrief Compare the group averages. Are the ratios close? π is defined as the ratio see “Mathematics connection” pg. 337 and The book of Pi

Using the number π Keep the number π in your answer if “exact answer” is required. Keep the number π in your calculations until the last step, to avoid rounding errors. It is best to use the π button on your calculator for your decimal approximation. If you don’t have a π button, you can substitute 3.14 for π.

Using the circumference conjecture 1) If a circle has a diameter 4.0 meters, what is the circumference? 2) If a circle has a circumference 20π, what is the radius? pg. 337+: 1 – 12, 21, 22 Start your homework: pg. 337+: 1 – 12, 21, 22 write basic info, the formula, substitution, do math, (show your steps) and add units!!

Challenge Question Imagine a steel belt fitting tightly around Earth’s equator. Now imagine cutting the belt and splicing in a piece to make the belt 40 feet longer. Make the longer belt stand out evenly from the equator. (HINT- C earth ≈ miles) What’s the largest object that will fit under the belt: an atom? an ant? a large dog? an elephant? Explain your answer in complete sentences. You may make a sketch to help you think about it.

Exit Quiz Which is greater, the height of a tennis ball can or the circumference of the can? Explain your thinking in 3 – 5 complete sentences. Justify your answer using the results of our investigation and the definition of π.