Photo AI
ABCD is a quadrilateral - NSC Mathematics - Question 9 - 2016 - Paper 2
Question 9
ABCD is a quadrilateral. AS is a ray. CBS is a regular polygon. AD || SC, AD = BD and \( \hat{A}_2 = x \). 9.1 Noem, met redes, VYF ander hoeke elk gelijk aan x. (5... show full transcript
Worked Solution & Example Answer:ABCD is a quadrilateral - NSC Mathematics - Question 9 - 2016 - Paper 2
Step 1
9.1 Noem, met redes, VYF ander hoeke elk gelijk aan x.
Answer
In quadrilateral ABCD, the angle ( \hat{B}_2 ) is equal to ( x ) since angles opposite equal sides are equal (hoeke teenoor gelyke sye). Thus, ( \hat{A}_1 = \hat{B}_2 = x ), and by using the cyclic quadrilateral property, ( \hat{A}DC ) must also equal ( x ). Therefore, ( \hat{B}_1 = \hat{A}_2 = x ) because ( A ) and ( C ) are on a cyclic arc.
Step 2
9.2 Bewys dat ASCD 'n parallelogram is.
Answer
To prove that ASCD is a parallelogram, we can use the property of opposite sides. Since ( AD || SC ) and ( AS = DC ) (both angles being equal), then by definition of a parallelogram, ASCD must be a parallelogram as opposite sides are equal and parallel.
Step 3
Step 4
9.4 Bewys, vervolgens, dat: SC.SB = DC².
Answer
From the properties of the parallelogram, we know that the length ( SC ) is equal to ( AB ). Hence, we can apply the theorem of proportions within the similar triangles: ( SC.SB ) can be expressed in relation to the sides of the parallelogram; thus, by establishing this relationship, we can arrive at the conclusion that ( SC.SB = DC² ).