Transcript 39 – Unit 3
Geometry 47 Line notation and relationships 46 Measure , draw, and name angles 45 Angle Pairs 44 Identify polygons and quadrilaterals 43 Solids 42 Translation, rotation, reflection, and dilations 41 Missing angles in triangles 40 Classify s and s 39 Similarity and Congruence 38 Similar triangles and proportions 37 WP: Similar triangles and proportions Ice Cream Answer Puzzle - President The 22nd and 24th president of the United States had the same mother and the same father, but they were not brothers. How is this possible? Who was this??? 47a Line notation and relationships A line can be named by a lower case letter or by two points on that line. Use the figure to name a line containing point K. Answer: The line can be named as line a. There are three points on the line. Any two of the points can be used to name the line. 47b Line notation and relationships ***If you have a protractor, bring it to class!*** Means “Line” (Has No Endpoints) Means “Ray” (Has one endpoint) — Means “Line Segment” (Has two endpoints – Has a length) Means “Perpendicular” (Meets in a 90° angle or Right ) || Means “Parallel” (Follow same direction – Never intersect) Skew lines are in different planes and never intersect Ray Means Perpendicular (90°) Line Puzzle - Know bull If a daddy bull weighs 1,200 pounds and eats 12 bales of hay each day, and a baby bull, who weighs 300 pounds, eats 3 bales of hay each day, then how much hay should a mommy bull eat if she weighs 800 pounds? 46a Measure, draw, and name angles An angle is usually named by 3 noncollinear points Angles can be named with three points on the angle with the vertex in the middle or by the vertex point if it is the only angle with that vertex. LMN or NML or M are all correct L MLN or L etc are NOT correct 1 M N When referring to an angle you may also mark it with an arc. An angle may also be named by a number such as above. 1 46b Measure, draw, and name angles Acute – Less than 90° Right – Exactly 90° – Marked by a Small Obtuse – Greater than 90° but less than 180° Straight – Exactly 180° Complementary s – Two angles that add up to 90° (Right) Supplementary s – Two angles that add up to 180° (Straight) Adjacent s – Two angles with a common side and a common vertex A complete circle = 360° 46c Measure, draw, and name angles Measure each angle named and classify it as right, acute, or obtuse. a. CZD Answer: 150, obtuse b. CZE Answer: 90, right c. DZX Answer: 30, acute 46d Measure, draw, and name angles What is the measure of the following angle? Puzzle What orchestral device is not blown, bowed, plucked, or struck? 45a – Angle pairs Linear pair – Two angles that form a straight angle (180) Vertical Angles – Angles directly across from each other when two lines intersect – Vertical angles are congruent () *Complementary s – Two angles that add up to 90° *Supplementary s – Two angles that add up to 180° *Adjacent s – Two angles with a common side And a common vertex F G DEF and FEG form a Linear Pair D Vertical angles E Puzzle - Impossible Triangle 44a Identify polygons and quadrilaterals Polygon – “Poly” means many, “gon” means angles 3 sides - Triangle 4 sides - Quadrilateral 5 sides - Pentagon 6 sides - Hexagon 7 sides - Heptagon or septagon* 8 sides - Octagon *These are the most likely 9 sides - Nonagon polygons to be named on 10 sides - Decagon your final exam…. 11 sides - 11-gon Know these!!!!! 12 sides - Dodecagon* Is a circle a polygon? No 13 sides - 13-gon 44b Identify polygons and quadrilaterals >> >> Parallelogram – Both pairs of opposite sides || Properties Opposite sides are Opposite s are 44c Identify polygons and quadrilaterals Rectangle – Quadrilateral with 4 Rt. s Properties Opposite sides are - 2 pairs of || sides 44d Identify polygons and quadrilaterals Rhombus – Quadrilateral with all four sides Properties All properties of a parallelogram Diagonals are 44e Identify polygons and quadrilaterals Square – Both a rhombus and a rectangle Properties Four sides and four s 44f Identify polygons and quadrilaterals Trapezoid – Exactly ONE pair of || sides The || sides are called the bases The non-|| sides are called legs Isosceles Trapezoid – One pair of || Sides Both legs are congruent Both pairs of base angles are 44g Identify polygons and quadrilaterals A kite is basically two isosceles triangles Properties Diagonals form Rt. Angles Puzzle What is it you sit in, sleep in, and brush your teeth with? 43a Solids Polyhedron = “Poly” means many, “hedron” means faces Faces = Flat surfaces (polygons) Edges = Line where two faces meet Vertices = Point or corner where edges meet Prism = Has two bases that are || Named by the shape of the base 6 Faces 12 Edges 8 Vertices Pyramid = Has only one base and comes to a point Named by the shape of the base Is this a polyhedron? NO 43b Solids A net is simply a shape unfolded = = 43c Solids 43d Solids - Activity Tetrahedron Faces Vertices Edges Icosahedron Faces Vertices Edges Cube Faces Vertices Edges Octahedron Faces Vertices Edges Dodecahedron These shapes are called the Platonic Solids. Faces Vertices Edges Why are they special? What to they mean? Clock Trick 42a Trans, Rot, Refl, & Dilation Remember that ordered pairs describe a location in terms of x and y such that (x,y). These are always in alphabetical order Where is point A and M located? A (-3,4) M(1,2) Also recall the quadrant values II I III IV 42b Trans, Rot, Refl, & Dilation Translation is simply a movement of a shape Ex. Points (–8, 4), (–8, 9), (–2, 9), and (–2, 4) form a quadrilateral. Which graph displays the quadrilateral and its dotted translation 5 units to the right and 6 units down? 42c Trans, Rot, Refl, & Dilation Rotation is simply turning an object Ex. Draw the rotation image of the figure for a rotation of 270 clockwise around turning point D. 42d Trans, Rot, Refl, & Dilation Reflection simply “flips” or “reflects” an image over a line 42e Trans, Rot, Refl, & Dilation Dilation is when something changes in size Think of your eyes dilating - The pupil changes size The Scale Factor is by how much it changes size Ex. The dotted triangle is the image of the solid triangle under a dilation with center (0,0). What is the scale factor? 42f Trans, Rot, Refl, & Dilation Quiz tomorrow on sections 83-79 83 Line notation and relationships 82 Measure , draw, and name angles 81 Angle Pairs 80 Identify polygons and quadrilaterals 79 Solids 78 Translation, rotation, reflection, and dilations 15 Questions - 15 Points Puzzle If I have one and a half dozen kids, how many children do I have. (By the way, this is not true) 41a Missing angles in a triangle The sum of the interior angles of a triangle = 180° B 105 A 32 C A + B +C = 180° If mA=32 and mB= 105, What is the measure of C? 32 + 105 + C = 180° C = 180 - 32 - 105 C = 43 The measure of C = 43° 41b Missing angles in a triangle Solve for x. B Exterior x A 132° ?48° D • C 180-90-48= 42 x=42° •E 40 Classify s and s My friends party…… A friend of mine has three kids Product of their ages is 72 Sum of ages is house number Oldest child loves strawberry ice cream How old are his children? What is his house number? 40 Classify s and s 40a Classify s and s Triangles be classified by the measures of their angles Acute All angles are less than 90° Right One angle measures 90 ° Obtuse One angle is greater than 90 ° 40b Classify s and s Triangles can be classified by lengths of sides All sides and all Equilateral angles are Isosceles Two sides and two angles Scalene No sides and no angles Right Lengths a2+b2=c2 (c is the longest side) c Puzzle Carry’s mother had a rather unusual fixation for naming her four children. The first child was named Quarter, the second child was named Dimeone and the third child was named Nicholas. What was the fourth Childs name? 39a Similarity and congruence Congruent polygons ( ) are exactly the same shape and size Similar polygons ( ~ ) have corresponding angles and the corresponding sides are proportional. Same shape, different size. X B A W ABCD~WXYZ ~ D C Z We can conclude: A W B X C Y D Z Similarity Statement Y AB WX BC XY CD YZ DA ZW 39b Similarity and congruence One triangle is shown on the grid. Two coordinates for a second triangle are also shown on the grid. Using the two points on the graph, which coordinates will create another triangle that is similar to the triangle that is shown? [A] (–6, –2) [B] (–6, 5) [C] (–6, –7) [D] (–6, –5) 39c Similarity and congruence Which two figures are similar but not congruent? [A] 1 and 5 [B] 3 and 5 [C] 2 and 4 [D] 2 and 3 Triangles BFC and QVU are similar. Write a proportion correctly identifying the corresponding sides? 39d Similarity and congruence Which statement is false? [A] g ~k [B] a f [C] a ~f [D] a ~k 39e Similarity and congruence CDE ~ HGF . Find the measure of x. x=60° Puzzle Has anyone figured out the strawberry ice-cream question yet? A friend of mine has three kids Product of their ages is 72 Sum of ages is house number Oldest child loves strawberry ice cream How old are his children? What is his house number? 38a Similar s and proportions ~ Polygons have same shape, and proportional sides. X AD=2 and WZ=3, 9 B W 6 A 2 D 3 ~ C 3 Z 4.5 Y If AB=6, what is the length of WX? ___ 9 If YZ=4.5, what is the length of CD? ____ 3 38b Similar s and proportions Given that ABC ~ DEF, solve for x and y. If ABC ~ DEF, BC = 3 feet, EF = 12 feet, and FD = 1 foot, find AC. E 12 B A 3 ? C D F 1 38c Similar s and proportions ABC and XYZ are similar. If AB, BC, and AC are 6 inches, 11 inches, and 15 inches respectively, and XY is 9 inches, find XZ to the nearest tenth. X A ? 15 9 6 B 11 C Y Z Puzzle Don’t read the words below, just say the color they are printed in. RED YELLOW GREEN BLUE RED BLUE YELLOW GREEN 37a WP: Similar s and proportions Standing next to each other, a woman casts a 51.2-inch shadow and her 46-inch-tall daughter casts a 36.8-inch shadow. What is the height of the woman to the nearest inch? x 46 51.2 36.8 37b WP: Similar s and proportions Two ladders are leaning against a wall at the same angle as shown. How long is the shorter ladder? 37c WP: Similar s and proportions Ruby wants to find the height of the tallest building in her city. She stands 399 feet away from the building. There is a tree 32 feet in front of her, which she knows is 15 feet tall. How tall is the building? (Round to the nearest foot.) 37d WP: Similar s and proportions 37e WP: Similar s and proportions Michele wants to measure the height of the streetlight outside her house. She places a mirror on the ground 46 feet from the streetlight, then walks backward until she is able to see the top of the streetlight in the mirror. Her eyes are 5.4 feet above the ground, and she is 12 feet from the mirror. What is the height of the streetlight to the nearest tenth of a foot? x 5.4 46 12 37a WP: Similar s and proportions