MODULE 7

• DISCIPLINE • GOOD TASTE • EXCELLENCE
• Writer: Gemma Y. Bandoquillo
• Cover Illustrator: Joel J. Estudillo
• MATHEMATICS Quarter 3: Module 7 Proving Right Triangle Similarity
• Department of Education National Capital Region SCHOOLS DIVISION OFFICE MARIKINA CITY
• What I Need to Know

  Prove the conditions for similarity of triangles:

  • SAS similarity theorem
  • SSS similarity theorem
  • similarity theorem
  • right triangle similarity theorem
  • special right triangle theorems
• What I Know

  You can say that you have understood the lessons in this module if you can already

  • Prove the conditions for similarity of triangles:

  a. SAS, SSS, AA, AAA Similarity Theorem.

  b. Right Triangles

  c. Special Right Theorem
• Are the quadrilaterals similar?

  1. ABCD and EFGH ______

  2. ABCD and JKLM ______

  3. ABCD and NOPQ _____

  4. JKLM and NOPQ ______

  5. If the corresponding angles of two polygons are congruent, then are the polygons similar? _____

  6. If the corresponding sides of two polygons are proportional, then the two polygons similar? _______

  7. Two polygons are similar. Are they congruent? _______

  8. Two polygons are congruent. Are they similar? ________

  9. Are all regular polygons similar? ________

  10. Is an equilateral triangle similar to equiangular triangle? ____
• One of the productive things that people do during lockdown was to plant. The #plantitos and #plantitas are tending nationwide. A curious "plantito" wanted to find the height of a Rubber tree in their backyard. He measured both his shadow which is 7ft.long and the shadow of Rubber tree which is 82 feet long.
• Guide Questions:

  a. What are the two triangles formed by the man and a tree?

  b. If the height of the is 5'9", what is the height of the tree?

  Analysis: Do you think the man shadow method could possibly be used in finding the height of the Rubber tree?
• Given: AD intersect BE at C.

  AE ⊥ BE , BD ⊥ DA

  Prove: BD/CD = AE/CE
• AA and AAA Similarities in Triangles


  AA Similarity Theorem

  If two angles of one triangle are congruent to the two angles of another triangle, then triangles are similar.
• AAA Similarity Theorem


  If three angles of one triangle are congruent to the three angles of another triangle, then triangles are similar.