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Chapter 4

Chapter 4. Congruent Triangles . 4.1 Congruent Figures 4.2 Triangle Congruence by SSS and SAS 4.3 Triangle Congruence by ASA and AAS. Students Will be able to Recognize Congruent figures and their Corresponding Parts Prove two triangles are congruent using SSS and SAS

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Chapter 4

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  1. Chapter 4 Congruent Triangles

  2. 4.1 Congruent Figures4.2 Triangle Congruence by SSS and SAS4.3 Triangle Congruence by ASA and AAS • Students Will be able to • Recognize Congruent figures and their Corresponding Parts • Prove two triangles are congruent using SSS and SAS • Prove two triangles are congruent using ASA and AAS MA.912.G.4.4 andMA.912.G.4.5 and MA.912.G.4.5 MA.912.D.6.4 and MA.912.G.8.5

  3. Notes for 4.1-4.3 • In order to prove that two figures are congruent we need to make sure that all sides and all angles of one polygon are equal to all angles and sides of another polygon. • In order to do this, we must first be able to decide which sides and angles on one polygon match with the sides and angles of another polygon… we call these matching pieces “corresponding parts”. • If the polygons are congruent then the corresponding parts should be equal.

  4. Notes for 4.1-4.3 • Proving two polygons are congruent could take a lot of work. For example if we want to show that two triangles are congruent we would need to show that all 3 angles and all 3 sides of one triangle are equal to all 3 angles and all 3 sides of another triangle! This is 6 different pairs of congruent parts!!! • We can use Logic and a few theorems to make some short cuts.

  5. Notes for 4.1-4.3 • Theorem: 3rd Angles Theorem: If two angles of one triangle are congruent to two angles of another triangle then the 3rd angles of both must be congruent. • SSS Theorem: If 3 sides of one triangle are congruent to 3 sides of another triangle then the triangles are congruent • SAS Theorem: If 2 sides of one triangle and the included angle of the triangle are congruent to 2 sides and the included angle of another triangle then the two triangles are congruent

  6. Notes for 4.1-4.3 • ASA Theorem: If 2 angles of one triangle and the included side of the triangle are congruent to 2 angles and the included side of another triangle then the two triangles are congruent • AAS Theorem: If 2 Angles and 1 side of one triangle are congruent to 2 Angles and 1 side of another triangle then the triangles are congruent • Hypotenuse Leg Theorem: If two right triangles have congruent hypotenuses and another pair of equal sides then the two triangles are congruent

  7. Classwork/Home Learning • Page 222 #10-19, 35, 36, 39, 40, 41 • Page 231 #11-14, 17, 24-26, 35-38 • Page 238 #13, 16-18, 25, 32-35

  8. 4.4: Corresponding Parts of Congruent Triangles are Congruent4.5: Isosceles and Equilateral Triangles • Students will be able to: • Use Triangle Congruence and CPCTS to prove that parts of two triangles are Congruent • Use and apply the properties of isosceles and equilateral Triangles MA.912.G.4.4 andMA.912.G.4.5 and MA.912.G.4.5 MA.912.D.6.4 and MA.912.G.8.5

  9. Notes for 4.4 and 4.5 • Once you know that two triangles are congruent based on SSS, SAS, ASA, AAS and HL you can now make conclusions about specific corresponding parts of triangles. • If you know that two shapes are exactly the same size and exactly the same shape (ie: They are congruent) then it makes sense that specific angles and specific sides that are corresponding should be the same too… this is what CPCTC means.

  10. Notes for 4.4 and 4.5 • With Isosceles and Equilateral Triangles we know even more information because we know that sides are across from equal angles • This means that in an Isosceles triangle we have 2 equal sides and the two angles across from them are also equal. • In an equilateral triangle, all sides and all angels are equal and all angles measure 60 degrees.

  11. Classwork/Homework • Page 247 #6, 11-13, 23-26 • Page 254 #6-9, 16-19, 37-40

  12. 4.6: Congruence in Right Triangles4.7: Congruence in Overlapping Triangles • Students will be able to • Prove right triangles are congruent using the Hypotenuse Leg Theorem • Identify congruent overlapping triangles and use congruent triangle theorems to prove triangles are congruent. MA.912.G.4.4 andMA.912.G.4.5 and MA.912.G.4.5 MA.912.D.6.4 and MA.912.G.8.5

  13. Notes for 4.6 and 4.7 • Hypotenuse Leg Theorem: If two right triangles have congruent hypotenuses and another pair of equal sides then the two triangles are congruent • When figures are overlapped it may be useful to separate the figures and identify the shared parts

  14. Classwork / Home Learning • Page 262# 15, 29-31 • Page 268# 8-13, 17, 29-32

  15. Office Aid I am at a meeting in the main office… here’s your list of things to do: • Come and see me in the office first!!!! • At the back of the room there is a hole puncher and papers – please hole punch • Clean up my classroom • The baskets in the back have papers and folders please put the papers into the correct student folders. If the student has no folder, just leave out.

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