Prove that the lengths of altitudes drawn to equal sides of an isosceles triangle are also equal.

(i) ∠TRQ = ∠SQR?
(ii) If ∠TRQ = 30°, find the base angles of the ΔPQR.
(iii) Is ΔPQR an equilateral triangle?
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You are making a blueprint of your bedroom and you plan to use a scale factor of 18 . the actual width of your room is 14 feet and the actual length of your room is 16 feet. determine the width and length of your room on the blueprint. on the blueprint, your room will have a width of feet and a length of feet.

Lance lived in portugal and brazil for a total of 14 months to learn portuguese. he learned an average of 130 new words per month when he lived in portugal, and an average of 150 new words per month when he lived in brazil. in total he learned 1920 new words. write a system of equations to represent the situation. use x to represent portugal, and y to represent brazil

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.