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Exercise 9.9 A. 1. ABCD is a square. The diagonals intersect at O. FB. AE Prove that EO = FO. %3D B. B. C.

Exercise 9.9 A. 1. ABCD is a square. The diagonals intersect at O. FB. AE Prove that EO = FO. %3D B. B. C.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Extend your skills Exercise 9.9 A. ABCD is a square. 1. The diagonals intersect at O. AE = FB. E Prove that EO = FO. F B 2. ABCD is a rhombus. The diagonals intersect at O. OE = EC, BF = FC Prove that OFCE is a rhombus. D ABCD is a quadrilateral. AOC and DOB are diagonals and O is the centre of the circle. Prove that ABC = 90° in two different ways as follows: Let OÄB = x and OCB = y then (i) Consider the interior angles of AABC (ii) Express AÔD and CÔD in terms of x and y (iii) Consider what type of special quadrilateral ABCD is. 3. B D 4. O is the centre of the circle. FG = HE. Prove: a) FA = CE b) AB = DC c) ABCD is a parallelogram G C B 5. O is the centre of the circle. AT = BU = CV = DW. ATOVC and DWOUB are straight lines. ВОС - 90° Prove ABCD is a square. W V. D C
Transcribed Image Text:Extend your skills Exercise 9.9 A. ABCD is a square. 1. The diagonals intersect at O. AE = FB. E Prove that EO = FO. F B 2. ABCD is a rhombus. The diagonals intersect at O. OE = EC, BF = FC Prove that OFCE is a rhombus. D ABCD is a quadrilateral. AOC and DOB are diagonals and O is the centre of the circle. Prove that ABC = 90° in two different ways as follows: Let OÄB = x and OCB = y then (i) Consider the interior angles of AABC (ii) Express AÔD and CÔD in terms of x and y (iii) Consider what type of special quadrilateral ABCD is. 3. B D 4. O is the centre of the circle. FG = HE. Prove: a) FA = CE b) AB = DC c) ABCD is a parallelogram G C B 5. O is the centre of the circle. AT = BU = CV = DW. ATOVC and DWOUB are straight lines. ВОС - 90° Prove ABCD is a square. W V. D C
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