Geometry Chapter 6 Mid Chapter Test Study

Study Notes

Exterior Angles of Polygons

Measure of each exterior angle of a polygon: ( \frac{360}{n} ) where ( n ) is the number of sides.
Example: Measure of each exterior angle of a regular 56-gon is ( 6.4^\circ ).

Parallelogram Properties

In parallelogram ABCD, if given segments BE and ED, set equations equal for angle bisector: ( 2x + 6 = 5x - 12 ).
Solving yields ( x = 6 ); substitute back to find length of BD.

Slope in Parallelograms

For slopes PQ and QR, if PQ has slope ( \frac{2}{3} ) and QR has slope ( -\frac{1}{2} ), the slope of SR must equal that of PQ to maintain properties of a parallelogram.

Finding Angles in Parallelograms

Angle W is congruent to angle S in parallelogram rstw. Solve for W using x, where ( W = S ) and ( x = 17 ).

Interior Angles of Polygons

Total interior angles of a polygon: ( (n-2) \times 180 ).
For a 48-gon, the total interior angles are ( (48-2) \times 180 = 8280^\circ ).

Quadrilateral Interiors

Total interior angles of a quadrilateral is always 360°.
Solve equations for each angle and substitute for ( x ) if required; consider if all angles need to be found or just ( x ).

Example of Solving for Angles

Given ( 2x - 12 + 3x + 2 + x + 30 + x - 10 = 360 ), solve to find ( x = 50 ).

Angle Relationships in Parallelograms

In parallelogram ABCD, if ( \angle A = 138^\circ ), then ( \angle B = 180 - 138 = 42^\circ ).

Parallelogram Identification

A shape is a parallelogram if opposite sides are congruent and parallel. Use slope formula to check: ( \frac{y_2 - y_1}{x_2 - x_1} ) for opposite sides.

Angle Measure Example

Angles L and J, given their measures, are congruent due to a bisector. Their totals relate to adjacent angles being supplementary to ( 180^\circ ).

Verifying Polygon Sides

The number of angles in a polygon can be found inversely using: ( \frac{\text{given total}}{180} + 2 ). For 720°, this gives 6 sides; for 360°, it gives 4 sides.

General Tips for Geometry

Always draw diagrams for clarity, label components, utilize calculators wisely, and confirm understanding of questions before solving.

Description

Prepare for the Geometry Chapter 6 mid-chapter test with these flashcards. Learn how to find the measure of exterior angles of polygons and tackle example problems, including those related to parallelograms. This study aid emphasizes understanding the key concepts visually.