## ã1.7.cã Practice Problems

[Math Center] 1. A closed rectangular tank contains a certain amount of water. When the tank is placed on its [latex]3[latex] ft by [latex]4[latex] ft side, the height of the water in the tank is [latex]5[latex] ft. When the tank is placed on another side of dimensions [latex]4[latex] ft by [latex]5[latex] ft, what is the […]

## ã1.6.cã āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻā§āĻ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. In the [latex]xy[latex]-plane, the equation of line [latex]k[latex] is [latex]3x-2y=0[latex]. Quantity A Quantity B The [latex]x[latex]-intercept of line [latex]k[latex] The [latex]y[latex]-intercept of line [latex]k[latex]   2. In the [latex]xy[latex]-plane, lineÂ [latex]k[latex] is a line that does not pass through the origin. Which of the following statements individually provide(s) sufīŦcient additional information to determine […]

## ã1.5.cã Mixed Geometric Shapes

[Math Center] 1. In the īŦgure above, the diameter of the circle is [latex]10[latex]. Quantity A Quantity B The area of quadrilateral [latex]ABCD[latex] [latex]40[latex]   2. For the rectangular solid below, īŦnd the following. (a) Surface area of the solid (b) Length of diagonal [latex]AB[latex]   3. A circle is inscribed in a square with […]

## ã1.4.cã āĻŦāĻšā§āĻ­ā§āĻ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. Quantity A Quantity B The area of the shaded region [latex]36[latex]   2. In the rectangular solid above, and What is the area [latex]TU=3, UV=4, VR=2[latex]. of the shaded rectangular region?   3. [latex]A, B[latex], and [latex]C[latex] are three rectangles. The length and width of rectangle [latex]A[latex] are [latex]10[latex] percent greater and […]

## ã1.3.cã āĻŦā§āĻ¤ā§āĻ¤ āĻāĻŦāĻ āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. AB is a diameter of the circle. Quantity A Quantity B The length of [latex]AB[latex] The average (arithmetic mean) of the lengths of [latex]AC[latex] and [latex]AD[latex]   2. In the īŦgure above, [latex]O[latex] and [latex]P[latex] are the centers of the two circles. If each circle has radius [latex]r[latex], what is the area […]

## ã1.2.cã āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¤ā§āĻ°āĻŋāĻ­ā§āĻ, āĻ¤āĻžāĻĻā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1.   [latex]DFG[latex] is a straight line. What is the value of [latex]x[latex]? A. 12 B. 14 C. 16 D. 18 E. 20 2. If the hypotenuse of an isosceles right triangle is [latex]7\sqrt { 2 }[latex] , what is the area of the triangle? (A) [latex]14[latex] (B) [latex]18[latex] (C) [latex]24.5[latex] (D) [latex]28[latex] […]

## ã1.1.cã āĻā§āĻ¨, āĻ°ā§āĻāĻž āĻāĻŦāĻ āĻĻā§āĻ°āĻ¤ā§āĻŦ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1.   In the figure, lines [latex]l[latex] and [latex]m[latex] are parallel. If [latex]y-z = 60[latex], then what is the value of [latex]x[latex] ? (A) [latex]60[latex] (B) [latex]75[latex] (C) [latex]90[latex] (D) [latex]120[latex] (E) [latex]135[latex]   2.   In the figure, [latex]AD[latex] and [latex]BC[latex] are lines intersecting at [latex]O[latex]. What is the value of [latex]a[latex] […]

## ã1.7.aãāĻ¤ā§āĻ°āĻŋāĻŽāĻžāĻ¤ā§āĻ°āĻŋāĻ āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻŦāĻ¸ā§āĻ¤ā§ āĻŦāĻŋāĻˇā§āĻ āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻŋāĻ āĻĒā§āĻ°āĻļā§āĻ¨

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) GeometryÂ āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã7ãÂ 3D Objects āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.7.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.7.aãāĻ¤ā§āĻ°āĻŋāĻŽāĻžāĻ¤ā§āĻ°āĻŋāĻ āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻŦāĻ¸ā§āĻ¤ā§ āĻŦāĻŋāĻˇā§āĻ āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻŋ: Surface Area The surface area of a three-dimensional shape is the amount of space on the surface of that particular object. Surface areaÂ āĻŦāĻž āĻĒā§āĻˇā§āĻ āĻ¤āĻ˛ā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻāĻ¤āĻā§āĻā§ āĻ¤āĻž āĻŽāĻ¨ā§ āĻ°āĻžāĻāĻžāĻ° āĻ¸āĻšāĻ āĻ¨āĻŋā§āĻŽ āĻšāĻ˛ā§ āĻāĻ āĻŦāĻ¸ā§āĻ¤ā§āĻāĻŋāĻā§ […]

## ã1.4.aã āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻŦāĻšā§āĻ­ā§āĻ āĻāĻŦāĻ āĻ¤āĻžāĻĻā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ā§āĻ° āĻŦāĻŋāĻļāĻĻ āĻāĻ˛ā§āĻāĻ¨āĻž

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) GeometryÂ āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã4ã Polygons āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.4.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.4.aã āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻŦāĻšā§āĻ­ā§āĻ āĻāĻŦāĻ āĻ¤āĻžāĻĻā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ā§āĻ° āĻŦāĻŋāĻļāĻĻ āĻāĻ˛ā§āĻāĻ¨āĻž Introduction PolygonsÂ āĻŦāĻž āĻŦāĻšā§āĻ­ā§āĻ A polygon is defined as a closed shape formed by line segments. Three-sided shapes (Triangles) Four-sided shapes (Quadrilaterals) Other polygons with [latex]n[latex] sides (where [latex]n[latex] is five […]

## ã1.5.aã Mixed Geometric Shapes

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) GeometryÂ āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã5ãÂ Mixed Geometric Shapes āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.5.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.5.aã Mixed Geometric ShapesÂ (āĻ­āĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻŋāĻ āĻāĻžāĻ āĻžāĻŽā§āĻ° āĻāĻ˛ā§āĻāĻ¨āĻž) āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻ­ā§āĻ¤āĻ°ā§ āĻŦāĻ¨ā§āĻĻā§ āĻāĻ¤ā§āĻ°ā§āĻ­ā§āĻ āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻŽāĻ§ā§āĻ¯ā§ āĻāĻ¨ā§āĻ¤āĻ°ā§āĻ˛āĻŋāĻāĻŋāĻ¤ āĻāĻ¤ā§āĻ°ā§āĻ­ā§āĻā§āĻ° āĻŦāĻŋāĻĒāĻ°ā§āĻ¤ āĻā§āĻŖāĻĻā§āĻŦā§ā§āĻ° āĻ¯ā§āĻāĻĢāĻ˛ [latex]180[latex]0Â āĻšā§āĨ¤ āĻ¯ā§āĻŽāĻ¨, āĻāĻĒāĻ°ā§ āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻŽāĻ§ā§āĻ¯ā§ āĻāĻāĻāĻŋ āĻāĻ¤ā§āĻ°ā§āĻ­ā§āĻ āĻāĻāĻāĻž āĻšā§ā§āĻā§, āĻ¯āĻžāĻ° āĻāĻžāĻ°āĻāĻŋ āĻā§āĻŖ āĻšāĻ˛ā§ [latex]p, q, r, s[latex] āĨ¤ āĻ¤āĻžāĻšāĻ˛ā§, […]

## ã1.2ã(b) āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¤ā§āĻ°āĻŋāĻ­ā§āĻ āĻāĻŦāĻ āĻ¤āĻžāĻĻā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) GeometryÂ āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§ (2) Triangle āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.2.bãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.2ã(b) āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¤ā§āĻ°āĻŋāĻ­ā§āĻ āĻāĻŦāĻ āĻ¤āĻžāĻĻā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ Median āĻŦāĻž āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻ¤ā§āĻ°āĻŋāĻ­ā§āĻā§āĻ° āĻ¯ā§ āĻā§āĻ¨ āĻļā§āĻ°ā§āĻˇ āĻĨā§āĻā§ āĻŦāĻŋāĻĒāĻ°ā§āĻ¤ āĻŦāĻžāĻšā§āĻ° āĻŽāĻ§ā§āĻ¯āĻŦāĻŋāĻ¨ā§āĻĻā§āĻ° āĻ¯ā§āĻāĻ āĻ°ā§āĻāĻžāĻā§āĻ āĻŦāĻ˛ā§ āĻŽā§āĻĄāĻŋā§āĻžāĻ¨ āĻŦāĻž āĻŽāĻ§ā§āĻ¯āĻŽāĻžāĨ¤ It is the line segment joining any vertex of a triangle with the midpoint […]

## ã1.2 .aãāĻ¤ā§āĻ°āĻŋāĻ­ā§āĻ āĻĒāĻ°ā§āĻŦ ā§§āĻ āĻā§āĻŖ, āĻŦāĻžāĻšā§, āĻĒāĻŋāĻĨāĻžāĻā§āĻ°āĻŋā§āĻžāĻ¨ āĻ¸ā§āĻ, āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻ āĻŦāĻŋāĻļā§āĻˇ āĻā§āĻāĻ¸

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) GeometryÂ āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§ (2) Triangle āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.2 .aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.2 .aãāĻ¤ā§āĻ°āĻŋāĻ­ā§āĻ āĻĒāĻ°ā§āĻŦ ā§§āĻ āĻā§āĻŖ, āĻŦāĻžāĻšā§, āĻĒāĻŋāĻĨāĻžāĻā§āĻ°āĻŋā§āĻžāĻ¨ āĻ¸ā§āĻ, āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻ āĻŦāĻŋāĻļā§āĻˇ āĻā§āĻāĻ¸ Introduction: āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻĒāĻ°ā§āĻā§āĻˇāĻžā§ āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻŋÂ āĻāĻāĻļ āĻĨā§āĻā§ āĻ¤ā§āĻ°āĻŋāĻ­ā§āĻ āĻ¸āĻāĻā§āĻ°āĻžāĻ¨ā§āĻ¤ āĻĒā§āĻ°āĻļā§āĻ¨ āĻ¸āĻŦāĻā§ā§ā§ āĻŦā§āĻļāĻŋ āĻĨāĻžāĻā§āĨ¤ āĻ¸āĻŦāĻā§ā§ā§ āĻŦā§āĻļāĻŋ āĻā§āĻ°ā§āĻ¤ā§āĻŦāĻ°ā§āĻĒā§āĻŖ āĻšāĻ˛ā§ āĻ¸āĻŽāĻā§āĻŖā§ āĻ¤ā§āĻ°āĻŋāĻ­ā§āĻ āĻŦāĻž Right triangles (those with a [latex]90[latex]Â° angle)āĨ¤ […]

## ã1.6.aã āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻā§āĻ āĻŦāĻŋāĻˇā§āĻ āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻ āĻāĻ˛ā§āĻāĻ¨āĻž

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) GeometryÂ āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã6ãCoordinate Geometry āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.6.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.6.aã Coordinate Geometry (āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻā§āĻ āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻŋāĻ° āĻāĻ˛ā§āĻāĻ¨āĻž) Introduction: āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻĒāĻ°ā§āĻā§āĻˇāĻžā§Â āĻā§āĻŦ āĻāĻāĻāĻž coordinate geometry āĻĒā§āĻ°āĻļā§āĻ¨ āĻāĻ¸āĻ¤ā§ āĻĻā§āĻāĻž āĻ¯āĻžā§ āĻ¨āĻžāĨ¤ āĻ¤āĻžāĻ°āĻĒāĻ°ā§, āĻāĻŽāĻ°āĻž āĻāĻ āĻāĻ§ā§āĻ¯āĻžā§ā§ āĻāĻŋāĻā§ āĻŽā§āĻ˛āĻŋāĻ āĻŦāĻŋāĻˇā§ āĻ¨āĻŋā§ā§ āĻāĻ˛ā§āĻāĻ¨āĻž āĻāĻ°āĻŦā§ āĻ¯āĻžāĻ¤ā§ āĻ¸ā§āĻā§āĻĄā§āĻ¨ā§āĻāĻ°āĻž āĻĒāĻ°ā§āĻā§āĻˇāĻžā§ āĻ āĻ§āĻ°āĻŖā§āĻ° āĻĒā§āĻ°āĻļā§āĻ¨ āĻĻā§āĻā§ āĻŦāĻŋāĻĒāĻžāĻā§ āĻ¨āĻž āĻĒā§ā§āĻ¨āĨ¤ The Coordinate […]

## ã1.3.aã āĻŦā§āĻ¤ā§āĻ¤, āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻāĻŦāĻ āĻāĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) GeometryÂ āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã1.3ã Circle āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.3.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.3.aã āĻŦā§āĻ¤ā§āĻ¤, āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻāĻŦāĻ āĻāĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯ Introduction Circle āĻŦāĻž āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻĒā§āĻ°āĻ¤āĻŋāĻāĻŋ āĻŦāĻŋāĻ¨ā§āĻĻā§ āĻāĻāĻāĻŋ āĻ¨āĻŋāĻ°ā§āĻĻāĻŋāĻˇā§āĻ āĻŦāĻŋāĻ¨ā§āĻĻā§ (āĻā§āĻ¨ā§āĻĻā§āĻ° āĻŦāĻž center) āĻĨā§āĻā§ āĻ¸āĻŽāĻžāĻ¨ āĻĻā§āĻ°āĻ¤ā§āĻŦ āĻ°ā§āĻā§ āĻāĻ˛ā§āĨ¤ āĻ¨ā§āĻā§āĻ° āĻ¯ā§ āĻā§āĻ¨ āĻāĻāĻāĻŋ āĻāĻžāĻ¨āĻ˛ā§āĻ āĻŦā§āĻ¤ā§āĻ¤ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻā§ā§ āĻŦāĻžāĻā§ āĻ¤āĻĨā§āĻ¯āĻā§āĻ˛ā§ āĻŦā§āĻ° āĻāĻ°ā§ āĻĢā§āĻ˛āĻž āĻ¯āĻžā§āĨ¤ āĻ) circumference, āĻĒāĻ°āĻŋāĻ§āĻŋ […]