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Geometry Final Exam 2014 DPSA

Geometry Final Exam 2014 DPSA. Ms. DeGain. 3 rd card marking. Congruent Figures Congruent Triangles Properties of Polygons Properties of quadrilaterals. What is a congruent figure?. Corresponding sides and angles are same measure (congruent).

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Geometry Final Exam 2014 DPSA

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  1. Geometry Final Exam2014 DPSA Ms. DeGain

  2. 3rd card marking • Congruent Figures • Congruent Triangles • Properties of Polygons • Properties of quadrilaterals

  3. What is a congruent figure? • Corresponding sides and angles are same measure (congruent). • Corresponding is similar to matching sides and angles. • Look for tic marks and angle arcs, • Look for actual side measurements and angle measurements if available.

  4. Congruent Triangles • SSS: side, side, side • If three sides of one triangle are congruent to three sides of another triangle then the two triangles are congruent. • SAS: Side, Angle, Side • If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangles then the triangles are congruent.

  5. Congruence in triangles cont. ASA: Angle, Side, Angle AAS: Angle, Angle, Side • Two angles and an included side are congruent in two triangles. • Two angles and a non-included side are congruent in two triangles.

  6. Common Triangles Isosceles Equilateral • Sum of angles 180 • Two sides congruent • Two angles are congruent • BASE ANGLES are the same. • Sum of angles 180 • All angles are 60 degrees each. • Each side is congruent.

  7. Right Triangle Congruence • Hypotenuse-Leg Theorem (HL) • If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

  8. Polygon Properties • Polygon angle-sum theorem • Polygon exterior angle sum-theorem • Interior angle of regular polygon theorem • Classifying polygons • Equilateral • All sides congruent • Equiangular • All angles congruent • Regular • All sides and angles are congruent.

  9. Polygon prefixes • Tri • Quad • Penta • Hexa • Hepta • Octa • Nona • Deca • Dodeca • n

  10. Quadrilateral Properties • 4 sides • Sum 360 • 4 angles

  11. Parallelograms • Opposite sides are parallel • Opposite sides are congruent • Opposite angles are congruent • Consecutive angles are supplementary • Diagonals bisect each other

  12. Rectangles • Have all the properties of a parallelogram • Each angle is 90 degrees • Diagonals are equal in length

  13. Rhombi • All the properties of parallelograms • Four congruent sides • Diagonals are Perpendicular • Diagonals bisect each other • Diagonals bisect each angle

  14. Squares • Have all the properties of a parallelogram, rectangle and rhombus combined.

  15. Other quadrilaterals Trapezoids Kites • One pair of parallel sides • Bases • iSosceles have congruent base angles (2 pair) and 2 congruent sides • Two pairs of consecutive sides congruent • No opposite sides congruent • Diagonals are perpendicular

  16. Similarity • Corresponding angles are congruent • Corresponding sides are proportional • Scale factor = the ratio of similar figures • Similarity statement shows congruent angles, and proportional sides (extended ratio) • Similar symbol is ~

  17. Right Triangles Pythagorean Theorem Pythagorean Triples • “A” is a leg • “B” is a leg • “C” is they hypotenuse (longest side) • Whole numbers that satisfy the Pythagorean Theorem • Examples include: 3,4,5 and 6,8,10. • No Decimals • No fractions

  18. Special Right Triangles 45-45-90 30-60-90 • Both legs are the same exact measure. • If given a hypotenuse, use the following equation to solve for the leg: • There are two ways to find the short leg if It is missing: • Remember to reduce all fractions.

  19. Trigonometric Ratios Sine Cosine Tangent

  20. Area • Parallelograms • Squares • Rectangles • Triangles • Circles r stands for radius, and a radius ½ the diameter.

  21. Perimeter/circumference • Of Polygons: simply add all the sides! • Of circles: radius is the “r”, diameter is the “d”

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