9.3 Rectangles, Rhombuses and Squares

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9.3 Rectangles, Rhombuses and Squares Additional Example 4 Additional Example 5 Additional Example 6 © SNP Panpac (H.K.) Ltd.

Additional Example 4 In the figure, ABCD is a rectangle. Find a, b, c and d. Solution © SNP Panpac (H.K.) Ltd.

Solution AO = OD (property of rectangle) Additional Example 4 In the figure, ABCD is a rectangle. Find a, b, c and d. Solution AO = OD (property of rectangle)  AOD is an isosceles triangle. OAD = b (base s, isos. ) OAD + ADO + AOD = 180 ( sum of ) b + b + 60 = 180 2b = 120 b = 60 © SNP Panpac (H.K.) Ltd.

Solution AOB + 60 = 180 (adj. s on st. line) AOB = 120 AO = OB Additional Example 4 In the figure, ABCD is a rectangle. Find a, b, c and d. Solution AOB + 60 = 180 (adj. s on st. line) AOB = 120 AO = OB (property of rectangle)  AOB is an isosceles triangle. BAO = 3a (base s, isos. ) © SNP Panpac (H.K.) Ltd.

Solution OAB + ABO + AOB = 180 ( sum of ) 3a + 3a + 120 = 180 Additional Example 4 In the figure, ABCD is a rectangle. Find a, b, c and d. Solution OAB + ABO + AOB = 180 ( sum of ) 3a + 3a + 120 = 180 6a = 60 a = 10 © SNP Panpac (H.K.) Ltd.

Solution AO = OC (property of rectangle) c – 2 = 10 c = 12 OB = OC Additional Example 4 In the figure, ABCD is a rectangle. Find a, b, c and d. Solution AO = OC (property of rectangle) c – 2 = 10 c = 12 OB = OC (property of rectangle) d – 6 = 10 d = 16 © SNP Panpac (H.K.) Ltd.

Additional Example 5 In the figure, ABCD is a square. Find a, b and c. Solution © SNP Panpac (H.K.) Ltd.

Solution (property of square) a = 45 3b = 90 (property of square) Additional Example 5 In the figure, ABCD is a square. Find a, b and c. Solution (property of square) a = 45 3b = 90 (property of square) b = 30 CD = AD =　　 cm (property of square) © SNP Panpac (H.K.) Ltd.

Solution ADC = 90 (property of square)  AC2 = AD2 + CD2 Additional Example 5 In the figure, ABCD is a square. Find a, b and c. Solution ADC = 90 (property of square)  AC2 = AD2 + CD2 (Pyth. Theorem) = 100 = 10 cm © SNP Panpac (H.K.) Ltd.

Solution (property of square)  OC = 5 cm 3c + 2 = 5 3c = 3 c = 1 Additional Example 5 In the figure, ABCD is a square. Find a, b and c. Solution  OC (property of square) = 5 cm 3c + 2 = 5 3c = 3 c = 1 © SNP Panpac (H.K.) Ltd.

Additional Example 6 ABCD is a rhombus with ABD = 28 and AE  DC. Find w, x, y and z. Solution © SNP Panpac (H.K.) Ltd.

Solution DBC = ABD = 28 (property of rhombus) ADC = ABC Additional Example 6 ABCD is a rhombus with ABD = 28 and AE  DC. Find w, x, y and z. Solution DBC = ABD = 28 (property of rhombus) ADC = ABC (property of rhombus) x = ABD + DBC = 28 + 28 = 56 BDC =　　 = 28 (property of rhombus) © SNP Panpac (H.K.) Ltd.

Solution In DBC, BDC + DCB + CBD = 180 ( sum of ) Additional Example 6 ABCD is a rhombus with ABD = 28 and AE  DC. Find w, x, y and z. Solution In DBC, BDC + DCB + CBD = 180 ( sum of ) 28 + 28 + y = 180 y = 124 DFE = w (vert. opp. s) In FDE, FDE + DFE = AEC (ext.  of ) 28 + w = 90 w = 62 © SNP Panpac (H.K.) Ltd.

Solution In ADE, DAE + ADE = 90 (ext.  of ) z + x = 90 Additional Example 6 ABCD is a rhombus with ABD = 28 and AE  DC. Find w, x, y and z. Solution In ADE, DAE + ADE = 90 (ext.  of ) z + x = 90 z = 90 – x = 90 – 56 = 34 © SNP Panpac (H.K.) Ltd.