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A Diagonal Inside

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 20 of 61.

A diagonal of a parallelogram crosses both pairs of parallel sides, so it makes alternate angles. In parallelogram ABCD with the diagonal AC, AB ∥ DC, so ∠BAC = ∠ACD. And AD ∥ BC, so ∠DAC = ∠ACB.

$Parallelogram with diagonal AC: the alternate angles BAC and ACD are both 35 degrees$

Here ∠BAC = 35°, so ∠ACD = 35° too. Each triangle the diagonal cuts off is a triangle like any other, so its three angles add up to 180°. Mixing the parallel rules with the triangle rules is how most quadrilateral problems are solved.

Challenge

ABCD is a parallelogram with the diagonal AC. The diagonal splits ∠DAB into 25° and 50°. Find ∠ADC, marked ?, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Polygons & Quadrilaterals

2Regular Polygons

Regular Polygons From an Angle to the Sides Inside a Regular Polygon Recap: Regular Polygons

5Rectangles, Rhombi, Squares

Rectangles The Diagonal of a Rectangle Rhombus Angles Squares Recap: Special Parallelograms

8Area of Parallelograms

Area of a Rectangle A Side from the Area Slide the Top Area of a Parallelogram Recap: Parallelogram Area

11Polygon Chases

Parallel Sides in a Pentagon Marks, Not Looks Pentagon with x Regular Shapes Together Recap: Polygon Chases