This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
a) If two triangles are congruent, then they have exactly same shape and size (True or False). True. Congruent triangles are defined as having the same shape and size. b) Any two equilateral triangles are congruent (True or False). False. While all equilateral triangles have the same shape (all angles are 60^), their sizes can differ. For example, an equilateral triangle with side length 2 cm is not congruent to an equilateral triangle with side length 5 cm. c) In the figure below, ABC DEF, A = 45^, C = 85^. Find the measures of D and E. Step 1: Use the property of congruent triangles to find D. Since ABC DEF, their corresponding angles are equal. Therefore, A = D. Given A = 45^. D = 45^ Step 2: Find B in ABC. The sum of angles in a triangle is 180^. A + B + C = 180^ 45^ + B + 85^ = 180^ 130^ + B = 180^ B = 180^ - 130^ B = 50^ Step 3: Use the property of congruent triangles to find E. Since ABC DEF, their corresponding angles are equal. Therefore, B = E. From Step 2, B = 50^. E = 50^ The measures are: D = 45^, E = 50^