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If measure of opposite angles of a parallelogram are (60 − x)° & (3x − 4)°, find the measures of angles of the parallelogram.
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M,N & P are the mid-points of sides AB, AC & BC of a △ ABC respectively. If MN= 3 cm, NP= 3.5 cm and MP= 2.5 cm, calculate BC, AB & AC respectively.
ABCD is a rhombus and P,Q,R,S are mid-points of AB, BC,CD and DA respectively. Prove that quadrilateral PQRS is a rectangle.
In the middle of the city, there was a park ABCD in the form of a parallelogram form so that AB = CD, AB||CD and AD = BC, AD||BC. Municipality converted this park into a rectangular form by adding land in the form of △APD and △BCQ. Both the triangular shape of land were covered by planting flower plants.
ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle PAC and CD || AB. Show that (i) ∠ DAC = ∠ BCA and (ii) ABCD is a parallelogram.
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