Marks, Not Looks

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 51 of 59.

A figure fixes an angle only when a chain of rules reaches it from the labels and marks. Looks are not evidence: two sides that look parallel count only when chevrons, or a rule, say so. And even true facts can leave an angle free.

$Trapezoid with AB parallel to DC marked by chevrons and 80 degrees at A$

Here the chevrons say AB ∥ DC, so ∠D is co-interior with ∠A: it is fixed at 100°. But ∠B and ∠C are not: the figure says nothing about the leg BC except that it joins the two bases, and the top corner C could slide along. Their sum is fixed, 180°, but neither one alone.

Challenge

Quadrilateral ABCD has ∠A = 85° and ∠B = 95°, with no other marks. Does the figure fix ∠C, marked ?, by itself? Answer, then press Check.

Try it yourself

$Is there enough information?$

Is there enough information?

All lessons in Polygons & Quadrilaterals

2Regular Polygons

Regular Polygons 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 PentagonMarks, Not LooksPentagon with x Regular Shapes Together Recap: Polygon Chases