What else would need to be congruent to show that triangle ABC is congruent to triangle DEF by ASA?
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We first need to divide the trapezium into a triangle(lets call it A) and a rectangle(lets call it B). We do this by marking a line colored red in the diagram given below from point B to E.
As one side of the rectangle is given length of 4cm, the parallel other must also be equal to 4cm. Hence, Length of A to E is equal to 11cm-4cm=7cm.
Now, we use this length of 7 cm as this is opposite to our desired angle(a colored green) and by making 16cm our hypotenuse we find angle a to be 25.9°.
Next we find angle b by adding angle a with 90. hence getting 115.9°.
Finally we consider our triangle ABC to find the length of AC. We know one angle and length of two sides and can easily use cosine rule to find the remaining length AC. The equation and working is shown in diagram.
Answer= 18.1
As one side of the rectangle is given length of 4cm, the parallel other must also be equal to 4cm. Hence, Length of A to E is equal to 11cm-4cm=7cm.
Now, we use this length of 7 cm as this is opposite to our desired angle(a colored green) and by making 16cm our hypotenuse we find angle a to be 25.9°.
Next we find angle b by adding angle a with 90. hence getting 115.9°.
Finally we consider our triangle ABC to find the length of AC. We know one angle and length of two sides and can easily use cosine rule to find the remaining length AC. The equation and working is shown in diagram.
Answer= 18.1