Angles and Triangles

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1 nges nd Tringes n nge is formed when two rys hve ommon strting point or vertex. The mesure of n nge is given in degrees, with ompete revoution representing 360 degrees. Some fmiir nges inude nother fmiir nge woud e right nge, whih mesures stright nge whih mesures 90 degrees. 80 degrees. 90 o 80 o n ute nge is n nge, whih mesures etween 0 nd 90 degrees. n otuse nge is n nge, whih mesures etween 90 nd 80 degrees. When two ines interset, if the mesure of one nge is known then nges n e determined sine stright nge mesures 80 degrees. In other words the sum of the mesure of two djent nges wi mesure 80 degrees. 43 o In the ove figure, given the 43 degree nge, we n ute the mesure of nge y sutrting 43 degrees from 80 degrees to otin 37 degrees. In simir fshion we n ute nge s 43 degrees nd nge s 37 degrees. Notie tht the djent nges dd up to 80 degrees whie verti nges (nges on opposite sides of intersetion) hve the sme mesure. simir sitution rises when pre ines re interseted y ine ( ed trnsvers ). It seems ogi tht when this ours the nges reted y the trnsvers with eh pre ine woud e the sme. In other words it seems tht the trnsvers woud interset eh of the pre ines t the sme nge. This is the se. In the ove figure nge nd nge woud e the sme. Then ike the interseting ines disussed erier, if the mesure of one nge is known, in the se of pre ines ut y trnsvers, then the mesure of nges oud e uted sed on the stright nge whih mesures 80 degrees.

2 tringe is osed three-sided figure. The sum of the three inside nges of tringe wi mesure 80 degrees. In ddition, the rgest inside nge wi e opposite the ongest side nd the smest inside nge wi e opposite the shortest side. The inside nges of tringe re proportion to opposite sides. right tringe is tringe with one inside nge tht mesures 90 degrees. The tringe ove is right tringe. The right nge ( 90 degrees )is usuy represented s squre insted of n r. The side of the tringe opposite the right nge is ed the hypotenuse nd is the rgest side. The other two sides of the tringe re simpy referred to s egs. The Pythgoren theorem retes the ength of the sides of right tringe with the foowing formu. =+, where is the ength of the hypotenuse, nd nd represent the two egs. The Pythgoren Theorem is used to find the missing side of right tringe when the other sides re known. 8 ft. ft. For the ove figure, the missing side is the hypotenuse, whih n e found using the Pythgoren theorem. =+ =8+ =64+44 =08 = 08 ft. or 4.4 ft. if rounded to the nerest hundredth of foot. 7 m. 9 m. For the ove figure, the missing side is one of the egs, whih n e found using the Pythgoren theorem. =+ 7 = +9 =7-9 =79-36 =368 = 368 m. or 9.8 m. rounded to the nerest hundredth of meter.

3 n isosees tringe is tringe with two sides equ. The inside nges opposite the equ sides re so equ. Tringe ove is n isosees tringe. Sides nd re equ s re inside nges nd. n equiter tringe hs sides equ s we s nges. For the equiter tringe ove, the sides re equ nd eh inside nge mesures 60 degrees.

4 Proem Set : Find the mesure of nges nd for the figures eow... nd re pre o 4 65 o Find nge for the figures eow. 3. nge =08 nd nge = nge =37 5. Side is equ to side 6. sides re equ 3 o Find the unknown side for eh tringe eow. Round nswer to nerest hundredth ft. 3 m. 56 m. 33 ft ft. 7 in. 46 in. 9 ft.

5 Proem Set : Find the mesure of nges nd for the figures eow... nd re pre 37 o 3. For the figure eow, find the 4. Tringe is n isosees tringe mesure of nges nd E. with side equ to side. nge Tringe is n equiter mesures 35 degrees. Wht re tringe nd ine DE is pre the mesures of nges nd to ine. E. D E D 36 o E The tringe eow is n isosees right tringe. 5. Find the mesure of nge. 6. Find the ength of side. 50 ft. Use the tringe eow for proems 7 to 0. Round nswer to nerest hundredth. 7. Given: = 9, =, Find. 8. Given: = 7, = 3, Find. 9. Given: = 0, =, Find. 0. Given: = 6, = 8, Find.

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