* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Geometry Chapter 7 Blank Notes - Copley
Survey
Document related concepts
Multilateration wikipedia , lookup
Line (geometry) wikipedia , lookup
Euler angles wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Noether's theorem wikipedia , lookup
RiemannβRoch theorem wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
List of works designed with the golden ratio wikipedia , lookup
Rational trigonometry wikipedia , lookup
History of geometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Golden ratio wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Transcript
7.1: _________________________________________________ Geometry Date: __________ A ___________ is a comparison of two quantities by _________________. You can write the ratio of two numbers in three ways: Ex 1). A pigmy rattlesnake has an average length of 18 in., while a Western diamondback rattlesnake averages a length of 5 ft 6 in. What is the ratio of the length of a pigmy rattlesnake to the length of a Western diamondback rattlesnake? Ex 2). Write the ratio of the first measurement to the second measurement. a) length of car: 14 ft 10 in length of model car: 8 in b) weight of car: 2900 lb weight of model car: 8 oz Ex 3). There are 238 juniors at a high school. The ratio of girls to boys in the junior class to is 3 : 4. How many juniors are girls? How many are boys? Ex 4). The measures of two complementary angles are in the ratio 1 : 3. What are the measures of the angles? Ex 5). The measures of two supplementary angles are in the ratio 1 : 4. What are the measures of the angles? An ______________ that states that two ratios are ________ is a ___________________. Solving Proportions Ex 6). Solve each proportion. a) 3 8 c) π¦+3 12 5 =π₯ = 5 6 b) 9 2 d) 15 π+1 π₯ = 14 = 3 π Ex 7). Write and solve a proportion. a) About 45 of every 300 apples picked at Newbury Apple Orchard are rotten. If 3560 apples were picked one week, about how many apples were rotten? b) A grocer orders 800 gal of milk each week. He throws out about 64 gal of spoiled milk each week. Of the 9600 gal of milk he ordered over three months, about how many gallons of spoiled milk were thrown out? Homework: pg. 459 #1, 3, 5, 9 β 13, 17 β 23 7.1 Day 2: ____________________________________________________ Date: __________ Geometry An _____________ ratio compares three (or more) numbers. Ex: Suppose an extended ratio of apples oranges to bananas is given as 2 : 3 : 5. apples oranges bananas 2 3 5 4 6 10 6 9 15 8 12 20 Ex 1). Using an extended ratio: a) The lengths of the sides of a triangle are in the extended ratio 2 : 4 : 5. The perimeter of the triangle is 77 in. What is the length of the longest side? b) The lengths of the sides of a triangle are in the extended proportion 3 : 4 : 10. If the length of the shortest side is 9 in., what is the perimeter of the triangle? Properties of Proportions (1) (2) (3) π₯ π¦ π₯ Ex 2). In the diagram, 10 = 9 . What ratio completes the equivalent proportion π¦ = the Properties of Proportions to justify your answer. Homework: pg. 459 #2, 4, 6, 14, 16, 24 β 30 ? Use one of 7.2: ________________________________________________ Geometry Date: __________ ______________ _____________ have the same ________ but not necessarily the same _______. Abbreviate is similar to with ________. Similar Polygons: βTwo polygons are similar if corresponding angles are _____________ and corresponding sides are _____________________.β A __________ ___________ is the ratio of corresponding sides. Ex 1). βππ π ~ βπ·πΈπΉ a). What are the pairs of congruent angles? b). What is the extended proportion for the ratios of corresponding side lengths? Ex 2). Are the polygons similar? If they are, write a similarity statement and give the scale factor. a) ABC and FED Ex 3). ABCD ~ MNOP. What is the value of x? b) LMNO and QRST Ex 4). WXYZ ~ RSTZ. What is the value of x? Ex 5). Jan uses an overhead projector to enlarge a picture 5 in. high and 7 in. wide. She projects the picture on a blackboard 4 ft 2 in. high and 12 ft wide. What are the dimensions of the largest picture that can be projected on the blackboard? Homework: pg. 468 #1 β 4, 6, 9 β 12, 14 β 16, 35 7.3: _________________________________________________ Geometry Date: __________ Postulate 7-1: Angle-Angle Similarity ( __________ ) Postulate βIf two angles of one triangle are ______________ to two angles of another triangle, then the triangles are _______________.β Ex 1). Are the two figure similar? How do you know? a) βπ ππ ~ βπππ b) βπΊπ»π ~ βπ·πΈπΉ Theorem 7-1: Side-Angle-Side Similarity ( ___________ ) Theorem βIf an angle of one triangle is _____________ to an angle of a second triangle, and the sides that include the two angles are ___________________, then the triangles are similar.β Theorem 7-2: Side-Side-Side Similarity ( ____________ ) Theorem βIf the corresponding sides of two triangles are ____________________, then the triangles are similar.β Ex 2). Are the triangles similar? Explain why. And if so, write a similar statement. a) b) c) Ex 4). Benjamin places a mirror 40 ft from the base of an oak tree. When he stands at a distance of 5 ft from the mirror, he can see the top of the tree in the reflection. If Benjamin is 5 ft 8 in. tall, what is the height of the oak tree? Homework: pg. 479 #1 β 3, 5, 7 β 10, 15, 16, 20, 21 7.4: _________________________________________________ Geometry Date: __________ Theorem 7-3: βThe altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are _____________ to the original triangle and to each other.β Ex 1). What similarity statement can you write relating the three triangles in the diagram? For any two positive numbers a and b, the ________________ _________ of a and b is the positive number x such that: Ex 2). What is the geometric mean of 5 and 12? Ex 3). What is the geometric mean of 25 and 4? Corollary 1 to Theorem 7-3: Ex 4). What are the values of x and y? Ex 6). What is the width of the kite? Homework: pg. 490 #1 β 6, 10, 12 β 18, 19, 32 Corollary 2 to Theorem 7-3: Ex 5). What is the value of x? 7.5: ________________________________________________ Geometry Theorem 7-4: Side-Splitter Theorem βIf a line is ____________ to one side of a triangle and intersects the other two sides, then it divides those sides _________________________.β Ex 1). What is the value of x in the diagram? Ex 2). What is the value of x in the diagram? Corollary to the Side-Splitter Theorem βIf three parallel lines intersect two __________________, then the segments intercepted on the transversals are _________________________.β Ex 3). Two plots of land are shown below, what is the unknown length, x? Date: __________ Ex 4). Find the value of x. Theorem 7-5: Triangle-Angle-Bisector Theorem βIf a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are ______________________ to the other two sides of the triangle.β Ex 5). Find the value of x in the diagram. Ex 6). Find the value of x in the diagram. Homework: pg. 500 #1 β 5, 8 β 24(e), 31, 32