Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Document
Document related concepts
Multilateration wikipedia , lookup
Dessin d'enfant wikipedia , lookup
Technical drawing wikipedia , lookup
Penrose tiling wikipedia , lookup
Noether's theorem wikipedia , lookup
History of geometry wikipedia , lookup
Apollonian network wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Euler angles wikipedia , lookup
Rational trigonometry wikipedia , lookup
List of works designed with the golden ratio wikipedia , lookup
Golden ratio wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Euclidean geometry wikipedia , lookup
Transcript
Homework Check: ππ ππ ππ ππ P 376 9. yes, KLMJ similar to PQNO ratio 3:5 10. Yes ABCD similar to FGHE 4:5 11. No corresponding angles are not congruent 13 x=4, y=3 15. X = 16, y= 4.5, z = 7.5 π π ππ = π π π ππ = π π π = π ππ π π = π π π ππ = π π Homework Check: π ππ = π π π ππ = π π ππ = ππ 15π = ππ π = π. ππ π = π. π π" π ππ π = π. π π ππ = π. π π ππ" π»ππ πππ πππ ππ ππ ππππππ ππππ π. π" π π " π π. πππ = πππ π. πππ ππ ππ π πππππ = π = π #ππ. π: π = π: π #ππ. π: π = π: π ππ β ππ β π π. π π 7π β π. π πππ = ππ π = ππ ππ + π = ππ π πππ β ππ β ππ = π = ππ π π. π = π. π π π = π. π ππ 49. Yes. The ratios of radii, diameters and circumferences are = 50. Examples from classβ¦ Proving Triangles Similar 7.3 Name the postulate or theorem used to prove congruency in the pairs of triangles to the right. Are there any that cannot be proven congruent? B AA C F E D G H I 2 figures are similar if: Corresponding angles are congruent, corresponding sides are proportional. Construct two lines of different lengths. Name the line segments AB and DE. π΄ π΅ π· πΈ Using your protractor, draw a 50o angle from A and D. πΉ πΆ 50° 60° 5° 50° πΊ 50° 50° π΄ 60° π΅ π· πΈ Using your protractor, draw a 60o angle from B and E. Label the points of intersection C and F πΆ πΉ 60° 60° π΄ π΅ π· πΈ Measure the sides of each triangle to the nearest mm. Find the ratio of the lengths of each pair of corresponding sides. πΆ πΉ 50° π΄ 50° 60° π΅ π· Based on your findings, what can you theorize? 60° πΈ Angle-Angle Similarity ( AA~) Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. πΆ βπ΄π΅πΆ~βπ·πΈπΉ 50° π· πΉ 60° πΈ πΊ π΄ 50° 60° π΅ 45° Can the triangles be proven similar? What are theorems or postulates that are used? Can you find the similarity ratio? 45° Side-Angle-Side Similarity ( SAS~) Theorem If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar. π π΄ π΄π΅ π΄πΆ = ππ ππ π΅ πΆ πΊ βπ΄π΅πΆ~βππ π π π Side-Side-Side Similarity ( SSS~) Thoerem If the corresponding sides of two triangles are proportional, then the triangles are similar. π΄ π π΄π΅ π΄πΆ π΅πΆ = = ππ ππ π π π΅ βπ΄π΅πΆ~βππ π π π πΆ Are the triangles similar? If so, write a similarity statement, name the postulate or theorem used, and tell the similarity ratio. π ππ 6 3 = = ππ 8 4 π π π 3 = ππ 4 β π β β π 8 π 6 π π π 4 3 β πππ ~βπππ ππ¦ ππ΄π~πβπππππ π ππ‘ππ 3: 4 π΄π 3 = π΄π΅ 8 Are the triangles similar? If so, write a similarity statement, name the postulate or theorem used, and tell the similarity ratio. π΄π½ 2 3 = = π΄πΆ 5 1 8 3 π΄ 3 2 π π΄π½ 3 = 2 β 16 π΄πΆ π½ 3 5 π΅ π΄π½ 2 = π΄πΆ 16 3 8 1 3 3 πΆ ππ½ 3 = π΅πΆ 8 β π΄ β β π΄ β ππ΄π½~βπ΅π΄πΆ ππ¦ πππ~ ππ ππ΄π~πβπππππ π ππ‘ππ 3: 8 Using similarity to determine unknown lengthsβ¦ MN/PQ=NO/QR Using similarity to determine unknown lengthsβ¦ Ann is 5 ft 5 in tall and casts a 5 ft shadow. The lamppost casts a 7 ft shadow. How high is the lamp-post? π΄π΅ πΆπ΅ = π·πΈ πΈπΉ 84 πΆπ΅ = 60 65 91β or 9 ft 5 inches. Homework: P385-387 1-4 all, 8, 9, 10-14 even, 17, 19, 30,, 34 Quiz over ratios, proportions, similar polygons, golden ratio, proving triangles similar.
