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Chapter 4 Congruent Triangles. Identify the corresponding parts of congruent figures Prove two triangles are congruent Apply the theorems and corollaries about isosceles triangles. 4.1 Congruent Figures. Objectives Identify the corresponding parts of congruent figures.

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## Chapter 4 Congruent Triangles

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**Chapter 4Congruent Triangles**• Identify the corresponding parts of congruent figures • Prove two triangles are congruent • Apply the theorems and corollaries about isosceles triangles**4.1 Congruent Figures**Objectives • Identify the corresponding parts of congruent figures**What we already know…**• Congruent Segments • Same length • Congruent Angles • Same degree measure**F**E Congruent Figures Exactly the same size and shape. Don’t ASSume ! C B A D**Two figures are congruent if corresponding vertices can be**matched up so that: 1. All corresponding sides are congruent 2. All corresponding angles are congruent. Definition of Congruency**What does corresponding mean again?**• Matching • In the same position**Volunteer**• Draw a large scalene triangle (with a ruler) • Cut out two congruent triangles that are the same • Label the Vertices A, B, C and D, E, F**You can slide and rotate the triangles around so that they**MATCH up perfectly. ABC DEF A E C B F D**The order in which you name the triangles matters !**ABC DEF A E C B F D**Based on the definition of congruency….**• Three pairs of corresponding sides • Three pairs of corresponding angles 1. A D 1. AB DE 2. B E 2. BC EF 3. C F 3. CA FD**It is not practical to cut out and move the triangles around**** ABC XYZ**• Means that the letters X and A, which appear first, name corresponding vertices and that • X A. • The letters Y and B come next, so • Y B and • XY AB**CAUTION !!**Don't ASSume • If the diagram doesn’t show the markings or • You don’t have a reason • Shared sides, shared angles, vertical angles, parallel lines**White Boards**• Suppose TIM BER IM ___**White Boards**• Suppose TIM BER IM ER , Why ?**White Boards**• Corresponding Parts of Congruent Triangles are Congruent**White Boards**• Suppose TIM BER ___ R**White Boards**• Suppose TIM BER M R, Why?**White Boards**• Corresponding Parts of Congruent Triangles are Congruent**White Boards**• Suppose TIM BER MTI ____**White Boards**• Suppose TIM BER MTI RBE**White Boards**• If ABC XYZ m B = 80 m C = 50 Name four congruent angles**White Boards**• If ABC XYZ m B = 80 m C = 50 A, C , X, Z**White Boards**• If ABC XYZ Write six congruences that must be correct**White Boards**• If ABC XYZ 1. A X 1. AB XY 2. B Y 2. BC YZ 3. C Z 3. CA ZX**Remote time**• Always • Sometimes • Never • I don’t know**A. AlwaysB. SometimesC. NeverD. I don’t know**• An acute triangle is __________ congruent to an obtuse triangle.**A. AlwaysB. SometimesC. NeverD. I don’t know**• A polygon is __________ congruent to itself.**A. AlwaysB. SometimesC. NeverD. I don’t know**• A right triangle is ___________ congruent to another right triangle.**A. AlwaysB. SometimesC. NeverD. I don’t know**• If ABC XYZ, A is ____________ congruent to Y.**A. AlwaysB. SometimesC. NeverD. I don’t know**• If ABC XYZ, B is ____________ congruent to Y.**A. AlwaysB. SometimesC. NeverD. I don’t know**• If ABC XYZ, AB is ____________ congruent to ZY.**4.2 Some Ways to Prove Triangles Congruent**Objectives • Learn about ways to prove triangles are congruent**Don’t ASSume**• Triangles cannot be assumed to be congruent because they “look” congruent. and • It’s not practical to cut them out and match them up so,**We must show 6 congruent pairs**• 3 angle pairs and • 3 pairs of sides**WOW**• That’s a lot of work Isn't there a shortcut ?**Spaghetti Experiment**• Using a small amount of playdough as your “points” put together a 5 inch, 3 inch and 2.5 inch piece of spaghetti to forma triangle. • Be careful, IT’S SPAGHETTI, and it will break.**Compare your spaghetti triangle to your neighbors**• Compare your spaghetti triangle to my spaghetti triangle. What do you notice ?**We are lucky…..**• There is a shortcut • We don’t have to show • ALL pairs of angles are congruent and • ALL pairs of sides are congruent**If three sides of one triangle are congruent to the**corresponding parts of another triangle, then the triangles are congruent. SSS Postulate E B C D A F**Patty Paper Practice**5 inches 3 inches 2.5 inches**If two sides and the included angle are congruent to the**corresponding parts of another triangle, then the triangles are congruent. SAS Postulate E B C D F**If two angles and the included side of one triangle are**congruent to the corresponding parts of another triangle, then the triangles are congruent. ASA Postulate E B C D A F**The order of the letters MEAN something**• Is SAS the same as SSA or A$$ ?**Construction 2**Given an angle, construct a congruent angle. Given: Construct: Steps:**Construction 3**Given an angle, construct the bisector of the angle Given: Construct: Steps:**CAUTION !!**Don't ASSume • If the diagram doesn’t show the markings or • You don’t have a reason • Shared sides, shared angles, vertical angles, parallel lines**Remote Time**Can the two triangles be proved congruent? If so, what postulate can be used? A. SSS Postulate • SAS Postulate • ASA Postulate • Cannot be proved congruent • I don’t know**A. SSS PostulateB. SAS PostulateC. ASA PostulateD.**Cannot be proved congruentE. I don’t know

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