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GENERAL AND SPECIFIC COMPETENCIES IN MATHEMATICS III (Geometry) A. Geometry of Shape and Size 1. Demonstrate knowledge and skills related to undefined terms, angles, polygons and circle 1.1 describe the ideas of • point • line • plane 1.2 identify, and name the subsets of a line • segment • ray 1.3 name and identify the parts of an angle 1.4 determine the measure of an angle using a protractor 1.5 illustrate different kinds of angles • acute • right • obtuse 1.6 define, identify and illustrate different kinds of polygons according to the number of sides 1.6.1 identify the parts of a regular polygon (vertex angle, central angle, exterior angle) 1.7 differentiate convex and non-convex polygons 1.8 identify, illustrate and name • a triangle • its basic parts • its secondary parts 1.9 classify triangles according to • angles • sides 1.10 define, illustrate and name a quadrilateral and its parts 1.11 identify, illustrate and name the different kinds of quadrilaterals 1.12 determine • sum of the measures of the angles of a triangle • sum of the measures of the exterior angles of a quadrilateral • sum of the measures of the interior angles of a polygon 1.13 define, identify and name the terms related to the circle (radius, diameter and chord) 2. Manifest knowledge and skills in identifying and measuring plane and solid figures and applying these in solving real life problems 2.1 state and apply the formulas for the measurements of plane and solid figures

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perimeter of a triangle, square, and rectangle circumference of a circle area of a triangle, square, parallelogram, trapezoid, and circle surface area of a cube, rectangular prism, square pyramid, cylinder, cone, and a sphere • volume of a rectangular prism, triangular prism, pyramid, cylinder, cone, and a sphere 2.2 solve problems involving plane and solid figures B. Geometric Relations 1. Demonstrate knowledge and skills involving relations of segments and angles, sides and angles of a triangle, and angles formed by parallel lines cut by a transversal, and solve problems on the relationships between segments and between angles. 1.1 define and illustrate betweeness and collinearity of points 1.2 define, identify and illustrate the following: • congruent segments • midpoint of a segment • bisector of an angle 1.3 define, identify and illustrate the different kinds of angle pairs: • supplementary • complementary • congruent • adjacent • linear pair • vertical angles 1.4 define, identify and illustrate perpendicularity 1.5 identify and illustrate the perpendicular bisector of a segment 1.6 derive/apply relationships among the sides and angles of a triangle • exterior and corresponding remote interior angles of a triangle • triangle inequality 1.7 define and illustrate parallel lines 1.8 define and illustrate a transversal 1.9 identify the angles formed by parallel lines cut by a transversal 1.10 determine the relationship between pairs of angles formed by parallel lines cut by a transversal • alternate interior angles • alternate exterior angles • corresponding angles • angles on the same side of the transversal 1.11 solve problems using the definitions and properties involving relationships between segments and between angles 16

C. Triangle Congruence 1. Manifest ability to illustrate and apply the conditions for triangle congruence in solving real life problems 1.1 state and apply the properties of congruence • Reflexive Property • Symmetric Property • Transitive Property 1.2 use inductive skills to prove congruence between triangles 1.3 apply deductive skills to show congruence between triangles • SSS Congruence • SAS Congruence • ASA Congruence • SAA Congruence 1.4 prove congruence properties in an isosceles triangle using the congruence conditions in 1.3 • Congruent sides in a triangle imply that the angles opposite them are congruent • Congruent angles in a triangle imply that the sides opposite them are congruent • Non-congruent sides in a triangle imply that the angles opposite them are not congruent • Non-congruent angles in a triangle imply that the sides opposite them are not congruent 1.5 Prove inequality properties in an isosceles triangle 1.6 use the conditions triangles congruence to prove: • congruent segments • congruent angles 1.7 solve routine and non-routine problems D. Properties of Quadrilaterals 1. Manifest ability to solve practical problems involving types of quadrilaterals and their properties and the conditions that guarantee that a quadrilateral is a parallelogram 1.1 apply inductive/deductive skills to derive certain properties of the trapezoid • median of a trapezoid • base angles and diagonals of an isosceles trapezoid 1.2 apply inductive and deductive skills to derive the properties of a parallelogram • each diagonal divides a parallelogram into two congruent triangles • opposite angles are congruent • non-opposite angles are supplementary • opposite sides are congruent 17

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diagonals bisect each other

1.3 apply inductive and deductive skills to derive the properties of the diagonals of special quadrilaterals • rectangle • square • rhombus 1.4 verify sets of sufficient conditions which guarantee that a quadrilateral is a parallelogram 1.5 apply the conditions to prove that a quadrilateral is a parallelogram 1.6 solve routine and non routine problems E. Similarity 1. Demonstrate knowledge and skills in verifying and applying ratio and proportion, proportionality theorems, similarity between triangles and similarities in a right triangle 1.1 apply the fundamental law of proportion • Product of the means is equal to the product of the extremes 1.2 apply the definition of proportional segments to find unknown lengths 1.3 illustrate and verify the Basic Proportionality Theorem and its Converse 1.4 apply the definition of similar triangles in: • determining if two triangles are similar • finding the length of a side or measure of an angle of a triangle 1.5 state and verify the Similarity Theorems: • AA similarity • SSS similarity 1.6 apply the properties of similar triangles and the proportionality theorems to calculate lengths of certain line segments 1.7 apply the AA Similarity Theorem to determine similarities in a right triangle • In a right triangle the altitude to the hypotenuse divides it into two right triangles which are similar to each other and to the given right triangle 1.8 apply the definition of similar triangles to derive the Pythagorean Theorem • If a triangle is a right triangle, then the square of the hypotenuse is equal to the sum of the squares of the legs 1.9 derive the relationships between the sides of • isosceles right triangle • 30-60-90 triangle using the Pythagorean Theorem 1.10 solve problem involving similar triangles F. Circles 1. Demonstrate knowledge and skills related to circles, arcs and angles, tangent lines and tangent circles, and angles formed by tangent and secant lines 1.1 define and identify a minor and major arc of a circle

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1.2 determine the degree measure of an arc of a circle 1.3 define and identify a central angle 1.4 determine the measure of a central angle 1.5 define and identify an inscribed angle 1.6 determine the measure of an inscribed angle 1.7 state and apply the properties of a line tangent to a circle • If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency • If two segments from the same exterior point are tangent to a circle, then the two segments are congruent 1.8 determine the measure of the angle formed by the following: • two tangent lines • a tangent line and a secant line • two secant lines G. Plane Coordinate Geometry 1. Demonstrate knowledge and skills related to plane coordinate geometry 1.1 derive the equation of a line given two points of the line 1.2 determine algebraically the point of intersection of two lines 1.3 state and apply the definitions of • parallel lines • perpendicular lines 1.4 derive and state the Distance Formula using the Pythagorean Theorem 1.5 derive and state the Midpoint Formula 1.6 apply the Distance and Midpoint Formulas to find the • lengths of segments • unknown vertices or points 1.7 verify properties of • triangles • quadrilaterals using coordinate proof 1.8 derive/state the standard form of the equation of a circle from the general form 1.9 given the equation of a circle, find its center and radius 1.10 determine the equation of a circle given: • its center and radius • its radius and the point of tangency with a given line 1.11 solve routine and non-routine problems involving circles

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