Vertices and Sides Examples

Is the figure shown a quadrilateral?

You betcha. The figure has 4 sides, 4 vertices, and 4 angles. It's a quadrilateral by all counts.

How do we break a quadrilateral into two triangles?

We can break any quadrilateral into two triangles by drawing either of its two diagonals. We can split this quadrilateral in two different ways.

Three angles of a quadrilateral are 67°, 98°, and 142°. What is the measure of the last angle?

We know that all four internal angles of any quadrilateral have to add up to 360° no matter what. We can set up an equation that sets the sum of the measures of the four angles to 360°. Then, we can substitute the measures of the angles we already know and solve for the final remaining measure.

m∠1 + m∠2 + m∠3 + m∠4 = 360
67 + 98 + 142 + m∠4 = 360
307 + m∠4 = 360
m∠4 = 360 – 307
m∠4 = 53

So we know the final angle has a measure of 53°. Whoop-dee-doo.