## CSETMathGuru: THE Site for Single Subject Math

**What skills must one possess for Subtest II: Geometry?**

You must:

- Know the distance formula.
- Midpoint formula.

- Know symmetric of graphs with respect to the a axis, y axis, origin, line y = x, line y = -x.
- Know the points slope form, slope intercept form of equation of lines.
- Know the condition for parallel and perpendicular lines using slopes.
- Know properties of isosceles, equilateral, right triangles.
- Know and apply the Triangle Congruence Theorems: SSS, ASA, AAS, SAS, HL.
- Prove geometric theorems and propositions in Statement- Reason form as well as in coordinate form.
- Provide basic geometric theorems using Indirect Proof( Proof By Contradiction).
- Know properties of perpendicular and angle bisectors.
- Know theorems concerning concurrency of perpendicular bisectors, angle bisectors and medians of a triangle relating to acute, obtuse and right triangles.
- Know and apply theorems on triangle inequalities.
- Know properties of interior and exterior angles of convex polygons.
- Know properties of parallelograms, squares, kites, rectangles, rhombus relating their to their sides, angles and diagonals.
- Know formulae of area of basic quadrilaterals.
- Be able to identify transformations as isometrics.
- Be able to perform isometric transformations of points in the coordinate plane: Rotations about the origin as wall as about the other points: Reflection about lines x = a, y = b as well as y=mx + b: translations.
- Know and apply the Similarity Theorems: AA, SAS, SSS.
- Apply concepts of proportion and similarity in word problems relating to geometric situations.
- Be able to perform dilations of objects in the coordinating plane.
- Solve Right Triangle Trigonometry: Determine missing sides and angles for a triangle.
- Know properties of 30°-60°-90°∆s and 45°-45°-90° ∆s.
- Use Trigonometric Ratios to determine coordinates of points lying on the vertices of regular polygons.
- Know properties of circles relating to tangent, chords, secants and angle of intersection.
- Be able to determine the areas and perimeters of regular polygons using trigonometry.
- Know properties of perimeters and areas of similar polygons.
- Be able to determine angle measures, areas and arc lengths of sectors in circles.
- Be able to solve basic problems relating to geometric probability.
- Know the Pythagorean Theorem.
- Prove geometric theorems and propositions in Statements – Reasons form well as in coordinate form.
- Prove basic geometric theorems using Indirect Proof (i.e. Proof By Contradiction).
- Know formulae concerning surface area and volume of 3-dimensional solids: Prism, Cylinder, Cone, Pyramid and Sphere.
- Know properties of surface area and volume for similar solids.
- Calculate areas and volumes of simple and complex 3-dimensional solids.
- Know Euler's Theorem relating to the faces, sides and vertices of polyhedrons.
- Be able to Prove and Apply the Law of Sines and Cosines.

- Theorems on parallel lines: Consecutive Interior Angle Theorem, Alternate Interior Angle Theorem, Alternate Exterior Angle Theorem, Consecutive Interior Angle Theorem Converse, Alternate Interior Angle Theorem Converse, Alternate Exterior Angle Converse; that two lines are parallel using Converse Theorems
- Triangle Sum Theorem, Exterior Angle Theorem.
- Apply the theorems of Triangle Congruence to prove congruence of angles and sides
- Base Angles Theorem and its Converse for Isosceles triangles.
- Perpendicular Bisectors Theorem and its converse.
- Angle Bisector Theorem and its converse.
- Mid-Segment Theorem.
- Triangle Inequalities related to sides and angles of a triangle.
- Theorems relating to properties of Parallelogram: Opposite sides are congruent, Opposite angles are congruent, Consecutive angles are supplementary, Diagonals bisect each other.
- a Quadrilateral is a parallelogram: Converse Theorems of the Parallelogram Theorems
- Properties of Rhombus, Rectangle, Square, Kite and Trapezoid to their aspects viz. Diagonals, sides and angles.
- Pythagorean Theorem and Properties of Special Right Triangles (30°-60°-90° ∆s and 45°-45°-90° ∆s).

- Circle Theorems: Perpendicularity of Radius to the circle at the point of tangency; Tangents from external point being congruent;

- Inscribed Angle Theorem.
- Theorems about the chords of circles.
- Theorems about inscribed polygons: Triangle inscribed in a semicircle is a right triangle; Quadrilateral inscribed in a circle has its opposite angles supplementary.

- Interior and Exterior Angle Theorems for Angles of a Convex Polygon.