MODULE 9

• Discipline


  Good Taste<|>Excellence
• Writers: Roselyn R. Baracuso, Cover Illustrator: Joel J. Estudillo
• This module is for Grade 9 Mathematics, Quarter 3, on Problems Involving Similarity of Triangles and Right Triangles
• The module is divided into two lessons: Lesson 1 - Problems Involving Similarity of Triangles, Lesson 2 - Problems Involving Right Triangles
• After going through this module, you are expected to:

  • Solve problems that involve triangle similarity
  • Solve problems that involve right triangles
  • Appreciate the importance of triangle similarity and right triangles in solving real-life problems
• Solve problems that involve triangle similarity

  1. Understand the concept of similar triangles

  2. Apply the properties of similar triangles to solve problems
• Solve problems that involve right triangles

  1. Understand the properties of right triangles

  2. Apply the properties of right triangles to solve problems
• Problems involving similarity of triangles and right triangles

  • Determining height of a tree using shadow
  • Determining height of a cat's shadow
  • Determining width of a river
• Rubric for evaluating the solution: Completeness (4), Correctness (4), Neatness (2), Total (10)
• Constructing a road passing through Gingerbread Building

  1. Building is already abandoned and scheduled for demolition

  2. Road is to be parallel to the side of the triangular History Park that is not along the road
• x


  Unknown length
• 20/35 = x


  Resulting equation
• Applying cross multiplication

  20x = 230(35)
• Simplifying 230(35)

  20x = 8050
• Applying division

  x = 402.5
• Therefore, the length of the road is 402.5 meters
• Solve the given problem
• Simplify the following
• What I Have Learned
• Discipline, Good Taste, Excellence
• What I Can Do
• Aga


  Standing on the top of head of Lea's shadow
• Lea


  Height is 6 feet
• Aga is 5 feet tall


  Length of their shadows combined is 15 feet
• Find the length of Aga's shadow
• Choose the letter that corresponds to the correct answer
• Read and understand the problem, then answer the questions
• What is asked?
• What are the given facts?
• What mathematical equation can you generate from the problem?
• What is the solution to the problem?
• Supply the missing lengths
• Pythagorean Theorem

  a^2 + b^2 = c^2
• Can the carpenter accomplish his task? If yes, how. If no, explain why.
• Determine the length of the other side of the triangle
• Find the length of the diagonal of the coloring book
• A bird on top of a tree saw an earthworm on the ground. The angle formed from the worm to the tree is 60°. If the tree is 10√3 meters high, how far is the worm from the bird?
• A 20 feet ladder reaches the top of a wall with angle of 45°. How tall is the wall?
• Solve the following problems
• Complete the steps in solving the indicated problem by filling up the blanks