MediumMathematicsHigh School (9–10)GeometryNumerical

In the four-sided figure ABCD, AB = AD and the line AC bisects the angle BAD…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

In the four-sided figure $ABCD$ , $AB = AD$ and the line $AC$ bisects the angle $BAD$ . Show that $BC = DC$ . Then find the perimeter of $ABCD$ when $AB = 7\ \text{cm}$ and $BC = 9\ \text{cm}$ .

Need a reminder? The key ideaShow

Triangles are congruent when they fit exactly on each other. In $\triangle ABC \cong \triangle PQR$ the order of the letters shows which corners match, and by CPCT every matching side and angle is equal. SAS needs two sides and the angle between them. A common side is equal to itself.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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