X + 1 D
The diagram shows a pentagon.
It has one line of symmetry.
AE = 4x
B В
AB = 2x + 3
BC = x + 1
2x + 3
All these measurements are given in centimetres.
The perimeter of the pentagon is 21 cm.
A
4x
a) Write an equation, in terms of x, for the perimeter of the pentagon.
Your final line should be in the form ax + b = 21 where a and bare
whole numbers.
E
(3)
b) Find the value of x.
(2)
+
Total marks: 5

Statements reasons 1. ab ≅ cd; ad ≅ bc 1. given 2. ac ≅ ac 2. reflexive property 3. △adc ≅ △cba 3. ? 4. ∠dac ≅ ∠bca; ∠acd ≅ ∠cab 4. cpctc 5. ∠dac and ∠bca are alt. int. ∠s; ∠acd and ∠cab are alt. int. ∠s 5. definition of alternate interior angles 6. ab ∥ cd; ad ∥ bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3?