The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;
1. AB:BC = 5:3
2. AB:CD = 1:1
3. m∠A : m∠C= 1 : 4
4. m∠B:m∠C = 4:1
5. AD: Perimeter ABCD = 3:16
What is a ratio?
A ratio is a representation of the number of times one quantity is contained in another quantity.
The shape of the quadrilateral ABCD in the question = A parallelogram
Length of AB = 15
Length of BC = 9
Measure of angle m∠A = 36°
Therefore;
1. AB:BC = 15:9 = 5:3
2. AB ≅ CD (Opposite sides of a parallelogram are congruent)
AB = CD (Definition of congruency)
AB = 15, therefore, CD = 15 transitive property
AB:CD = 15:15 = 1:1
3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)
Therefore; m∠A = m∠C = 36°
∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)
Therefore; ∠A + ∠D = 180°
36° + ∠D = 180°
∠D = 180° - 36° = 144°
∠D = 144°
m∠A : m∠C = 36°:144° =1:4
m∠A : m∠C = 1:4
4. ∠B = ∠D = 144° (properties of a parallelogram)
m∠B : m∠C = 144° : 36° = 4:1
5. AD ≅ BC (opposite sides of a parallelogram)
AD = BC = 9 (definition of congruency)
The perimeter of the parallelogram ABCD = AB + BC + CD + DA
Therefore;
Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48
AD:Perimeter of the ABCD = 9 : 48 = 3 : 16
Learn more about ratios here:
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