Geometry

Quadrilaterals

Properties of Trapezoids (US) / Trapeziums (UK)

         

In the above diagram, quadrilateral ABCDABCD is a trapezoid with ADBC.\overline{AD} \parallel \overline{BC}. If ABC=60,OCD=20,\lvert{\triangle ABC}\rvert=60, \lvert{\triangle OCD}\rvert=20, what is the area of OBC?\triangle OBC ?

Note 11: The above diagram is not drawn to scale, and ABC\lvert \triangle ABC \rvert denotes the area of ABC.\triangle ABC.
Note 22: In the US a quadrilateral with one pair of parallel lines is called a "trapezoid." Elsewhere, a quadrilateral with one pair of parallel lines is called a "trapezium."

In the above diagram, quadrilateral ABCDABCD is a trapezoid with ABCD.\overline{AB} \parallel \overline{CD}. If α=73\alpha^\circ={73}^\circ and γ=135,\gamma^\circ={135}^\circ, what is the value of ωβ?\omega-\beta ?

Note: In the US a quadrilateral with one pair of parallel lines is called a "trapezoid." Elsewhere, a quadrilateral with one pair of parallel lines is called a "trapezium."

In the above diagram, quadrilateral ABCDABCD is a trapezoid with ADBC.\overline{AD} \parallel \overline{BC}. If AO:OC=1:3,OBC=54,\lvert{\overline{AO}}\rvert:\lvert{\overline{OC}}\rvert=1:3, \lvert{\triangle OBC}\rvert=54, what is the area of quadrilateral ABCD?ABCD ?

Note 11: The above diagram is not drawn to scale, and ABC\lvert{\triangle ABC}\rvert denotes the area of ABC.\triangle ABC.
Note 22: In the US a quadrilateral with one pair of parallel lines is called a "trapezoid." Elsewhere, a quadrilateral with one pair of parallel lines is called a "trapezium."

In the above diagram, quadrilateral ABCDABCD is an isosceles trapezoid with ADBC.\overline{AD} \parallel \overline{BC}. If l=7,α=25,β=115,l=7, \alpha^\circ={25}^\circ, \beta^\circ={115}^\circ, what is the value of x+y?x+y ?

Note 11: The above diagram is not drawn to scale.
Note 22: In the US a quadrilateral with one pair of parallel lines is called a "trapezoid." Elsewhere, a quadrilateral with one pair of parallel lines is called a "trapezium."

Trapezium ABCDABCD has ABAB parallel to DCDC. If DBC=23\angle DBC = 23 ^\circ and BCD=59\angle BCD = 59 ^\circ, what is ABD\angle ABD (in degrees)?

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