7. INVESTIGATE In the sketch O is the centre of the circle and C and ɓ are angles in segment AB of the circle (or: angles subtended by chord AB). D Prove that C-D. (Do not measure C and D, but use knowledge of Geometry facts and theorems to show why C-D.) Hint: Draw in AO and BO In the sketch below ABCD is a cyclic quadrilateral, ie a quadrilateral with all four of its sides chords of the circle. Measure each of the angles A B- 6- A Complete 180 and also: 180 Therefore: The angles of a cyclic 131 C D B quadrilateral are In the sketch PQRS is a cyclic quadrilateral. O is the centre of the circle and QO and OS are drawn Complete the following proof, also giving reasons for statements where required. 0,-2-angle [Reason: 161 R 0,-2-angle [Reason: ..0,+0,-2x angle +2xangle. s Also: Ò,+0, [Reason: 2x angle +2xangle angle +angle 171

7. INVESTIGATE In the sketch O is the centre of the circle and C and ɓ are angles in segment AB of the circle (or: angles subtended by chord AB). D Prove that C-D. (Do not measure C and D, but use knowledge of Geometry facts and theorems to show why C-D.) Hint: Draw in AO and BO In the sketch below ABCD is a cyclic quadrilateral, ie a quadrilateral with all four of its sides chords of the circle. Measure each of the angles A B- 6- A Complete 180 and also: 180 Therefore: The angles of a cyclic 131 C D B quadrilateral are In the sketch PQRS is a cyclic quadrilateral. O is the centre of the circle and QO and OS are drawn Complete the following proof, also giving reasons for statements where required. 0,-2-angle [Reason: 161 R 0,-2-angle [Reason: ..0,+0,-2x angle +2xangle. s Also: Ò,+0, [Reason: 2x angle +2xangle angle +angle 171

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter4: Quadrilaterals

Section4.3: The Rectangle, Square, And Rhombus

Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...

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