Question

8 multiple choice 2 points which quadrilateral does not always have congruent diagonals? rhombus rectangle isosceles trapezoid square 9 multiple choice 2 points find sin40° to three decimal places. 0.996 1.192 0.839 0.643

Explanation:

Question 8

• Rectangle: In a rectangle, the diagonals are always congruent. By the Pythagorean theorem, if \(l\) is the length and \(w\) is the width of a rectangle, the length of the diagonal \(d=\sqrt{l^{2}+w^{2}}\), and both diagonals have the same length.
• Isosceles trapezoid: In an isosceles trapezoid, the non - parallel sides (legs) are congruent. Using the property of congruent triangles (by SSS - Side - Side - Side congruence criterion for the triangles formed by the bases and the diagonals), the diagonals are congruent.
• Square: A square is a special case of a rectangle (where \(l = w\)). So, by the property of rectangles, its diagonals are congruent. The length of the diagonal of a square with side \(a\) is \(d = a\sqrt{2}\), and both diagonals are equal.
• Rhombus: A rhombus has all sides equal. The diagonals of a rhombus are perpendicular bisectors of each other, but they are not always congruent. For example, a non - square rhombus (where the angles are not \(90^{\circ}\)) has diagonals of different lengths. The lengths of the diagonals \(d_1\) and \(d_2\) of a rhombus are related to the side \(a\) and angles \(\theta\) and \(180^{\circ}-\theta\) by the formulas \(d_1 = 2a\sin\theta\) and \(d_2=2a\cos\theta\) (when \(\theta

eq45^{\circ}\), \(d_1
eq d_2\)).

Step1: Use a scientific calculator

Set the calculator to degree mode.

Step2: Calculate \(\sin40^{\circ}\)

Press the \(\sin\) button and then enter \(40\).

Answer:

A. rhombus

Question 9