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Module 1: Advanced Concepts in Angles and Lines

Topics Covered:

1. Properties of Parallel and Perpendicular Lines
2. Angles Formed by a Transversal:
   • Corresponding Angles
   • Alternate Interior and Exterior Angles
   • Consecutive Interior Angles
3. Angle Bisectors and Perpendicular Bisectors

Practice Questions:

1. If two parallel lines are cut by a transversal, find the measure of an angle if its corresponding angle measures 70∘70^\circ70∘.
2. Draw a pair of perpendicular lines and label them.
3. Prove that the sum of interior angles on the same side of a transversal is 180∘180^\circ180∘.

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Module 2: Properties of Triangles

Topics Covered:

1. Medians, Altitudes, and Centroid
2. Properties of an Isosceles Triangle
3. Inequalities in Triangles:
   • Triangle Inequality Theorem
   • Exterior Angle Theorem

Practice Questions:

1. In a triangle, prove that the sum of any two sides is greater than the third side.
2. Draw and label the medians of a triangle.
3. If one angle of a triangle is 120∘120^\circ120∘, find the measure of its exterior angle.

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Module 3: Quadrilaterals and Their Properties

Topics Covered:

1. Parallelogram Properties:
   • Opposite Sides and Angles
   • Diagonals Bisect Each Other
2. Rhombus, Rectangle, and Square:
   • Distinguishing Features
3. Trapezium and Kite Properties

Practice Questions:

1. Prove that the diagonals of a rectangle are equal in length.
2. Identify whether a quadrilateral with one pair of parallel sides is a trapezium.
3. Draw a kite and label its diagonals.

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Module 4: Circles

Topics Covered:

1. Properties of Chords
   • Perpendicular Bisector of a Chord
   • Equal Chords and Their Distances from the Center
2. Angle Subtended by an Arc
3. Cyclic Quadrilaterals

Practice Questions:

1. Prove that the perpendicular from the center of a circle to a chord bisects the chord.
2. If a chord is 8 cm long and 6 cm from the center, find the radius of the circle.
3. Prove that the opposite angles of a cyclic quadrilateral are supplementary.

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Module 5: Perimeter, Area, and Advanced Applications

Topics Covered:

1. Area of Triangles Using Heron’s Formula
2. Area of Special Quadrilaterals: Trapezium, Rhombus
3. Applications in Real-Life Problems

Practice Questions:

1. Find the area of a triangle with sides 7 cm, 8 cm, and 9 cm.
2. Calculate the area of a rhombus with diagonals of length 10 cm and 12 cm.
3. A rectangular garden is 20 m long and 15 m wide. Find its perimeter and area.

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Module 6: Advanced Coordinate Geometry

Topics Covered:

1. Slope of a Line
2. Equation of a Line:
   • Point-Slope Form
   • Slope-Intercept Form
   • Two-Point Form
3. Collinearity of Points

Practice Questions:

1. Find the slope of a line passing through points (2,3)(2, 3)(2,3) and (5,7)(5, 7)(5,7).
2. Write the equation of a line with slope 222 passing through (1,4)(1, 4)(1,4).
3. Determine if points (1,2),(3,4),(5,6)(1, 2), (3, 4), (5, 6)(1,2),(3,4),(5,6) are collinear.

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Module 7: Transformations

Topics Covered:

1. Translation of Figures
2. Rotation:
   • 90∘,180∘90^\circ, 180^\circ90∘,180∘ About the Origin
3. Reflection Across Axes

Practice Questions:

1. Reflect the point (2,−3)(2, -3)(2,−3) across the x-axis and y-axis.
2. Rotate a triangle 180∘180^\circ180∘ about the origin and plot its new coordinates.
3. Translate a square 5 units right and 3 units up.

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Module 8: 3D Geometry

Topics Covered:

1. Introduction to 3D Shapes: Cube, Cuboid, Sphere, Cylinder, Cone
2. Surface Area and Volume Formulas
3. Nets of 3D Shapes

Practice Questions:

1. Calculate the surface area and volume of a cylinder with a radius of 7 cm and height of 10 cm.
2. Draw the net of a cube with side length 4 cm.
3. Find the volume of a cone with a base radius of 5 cm and height of 12 cm.

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Module 9: Similarity and Congruence

Topics Covered:

1. Conditions for Similarity and Congruence
   • SSS, SAS, ASA, RHS for Congruence
   • AA, SSS, SAS for Similarity
2. Application of Similarity in Triangles
3. Basic Construction Problems

Practice Questions:

1. Prove that two triangles are similar using AA similarity.
2. Construct a triangle similar to a given triangle with a scale factor of 23\frac{2}{3}32​.
3. Identify whether two given triangles are congruent or similar.

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Module 10: Final Review and Project

Topics Covered:

1. Mixed Questions on Geometry Concepts
2. Real-Life Geometry Project:
   • Plan a Floor Layout
   • Create a Garden Design Using Geometric Shapes
3. Final Test Preparation

Mock Test Sample Questions:

1. Prove that the sum of opposite angles in a cyclic quadrilateral is 180∘180^\circ180∘.
2. Find the area of a triangle with vertices (1,2),(4,6),(7,2)(1, 2), (4, 6), (7, 2)(1,2),(4,6),(7,2) using coordinate geometry.
3. Write the equation of a line passing through (3,5)(3, 5)(3,5) and parallel to y=2x+1y = 2x + 1y=2x+1.

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Additional Materials

• Worksheets for Constructive Problems
• Graphing and Plotting Exercises
• Interactive Tools for Transformations
• Geometry Quizzes for Reinforcement

This intermediate syllabus builds on basic geometry concepts, introducing learners to more analytical and practical applications of geometry, preparing them for advanced topics and real-world challenges.