Math  /  Geometry

Question2ABCD2 A B C D is a rhombus of center OO, having a side of 4 cm and such that A^=60\hat{A}=60^{\circ}. I,J,KI, J, K and LL are the midpoints of [AD],[AB][A D],[A B], [BC][B C] and [CD][C D] respectively. 11^{\circ} Replace the symbol * by a point from the figure : a) AIundefined=Kundefined\overrightarrow{A I}=\overrightarrow{K^{*}} b) C=KOundefined\vec{C} * *=\overrightarrow{K O} c) WDundefined=JOundefined\overrightarrow{W_{D}}=\overrightarrow{J O} d) OL=J\vec{O} L=\vec{J} e) KBundefined=BIundefined\overrightarrow{K B}=\overrightarrow{B I} f) ODundefined=Bundefined\overrightarrow{O D}=\overrightarrow{B *} 22^{\circ} Name the vectors equal to IJundefined\overrightarrow{I J} and equal to AIundefined\overrightarrow{A I}. 33^{\circ} Construct vector ARundefined=DBundefined\overrightarrow{A R}=\overrightarrow{D B} and vector BPundefined=DAundefined\overrightarrow{B P}=\overrightarrow{D A}. What do you notice ? 44^{\circ} Answer by True or False. a) AIundefined=AJundefined\overrightarrow{A I}=\overrightarrow{A J} b) DLundefined=BKundefined\overrightarrow{D L}=\overrightarrow{B K} folse c) IJundefined=LKundefined\overrightarrow{I J}=\overrightarrow{L K} Tfue d) ARundefined=CDundefined\overrightarrow{A R}=\overrightarrow{C D} falsc e) ABundefined=CBundefined\overrightarrow{A B}=-\overrightarrow{C B} f) ADundefined=CBundefined\overrightarrow{A D}=-\overrightarrow{C B} True g) BIundefined=KDundefined\overrightarrow{B I}=\overrightarrow{K D}. True 55^{\circ} Complete by == or \neq a) ADundefinedCDundefined\|\overrightarrow{A D}\| \ldots\|\overrightarrow{C D}\| b) BCundefined=ADundefined\overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{AD}} c) IJundefinedKLundefined\overrightarrow{I J} \leftrightarrows \overrightarrow{K L} d) BJundefinedLDundefined\overrightarrow{B J} \therefore \overrightarrow{L D} e) IKundefinedJLundefinedmagit\|\overrightarrow{I K}\| \ldots\|\overrightarrow{J L}\|-\operatorname{mag} i t ade f) OIundefined.OKundefined\overrightarrow{O I} . \ldots \overrightarrow{O K} g) LOundefinedOJundefined\overrightarrow{L O} \doteqdot \overrightarrow{O J} h) CKundefined=IAundefined\overrightarrow{C K}=\overrightarrow{I A}. 66^{\circ} Complete by the convenient vector : a) The opposite of BCundefined\overrightarrow{B C} is CRC R b) Vectors AJundefined\overrightarrow{A J} and ......... are equal. c) Vectors LDundefined\overrightarrow{L D} and JRJ R. are opposite. \qquad d) The opposite of vector ABundefined+CDundefined\overrightarrow{A B}+\overrightarrow{C D} is 77^{\circ} Write ABundefined\overrightarrow{A B} as a sum of three vectors, then of four vectors. 88^{\circ} Calculate : a) AIundefined+IBundefined\|\overrightarrow{A I}+\overrightarrow{I B}\| b) ADundefined+OJundefined\|\overrightarrow{A D}+\overrightarrow{O J}\| c) AOundefined+BJundefined\|\overrightarrow{A O}+\overrightarrow{B J}\| d) ADundefined+CBundefined\|\overrightarrow{A D}+\overrightarrow{C B}\|.

Studdy Solution
a) AIundefined+IBundefined=ABundefined=4 cm\|\overrightarrow{A I} + \overrightarrow{I B}\| = \|\overrightarrow{A B}\| = 4 \text{ cm}. b) ADundefined+OJundefined=AOundefined+OJundefined=4 cm\|\overrightarrow{A D} + \overrightarrow{O J}\| = \|\overrightarrow{A O} + \overrightarrow{O J}\| = 4 \text{ cm}. c) AOundefined+BJundefined=ABundefined=4 cm\|\overrightarrow{A O} + \overrightarrow{B J}\| = \|\overrightarrow{A B}\| = 4 \text{ cm}. d) ADundefined+CBundefined=0 cm\|\overrightarrow{A D} + \overrightarrow{C B}\| = 0 \text{ cm} because they are opposite vectors.

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