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Proving Triangles Congruent Lesson 17 Question of the Day: Match the definition with a term from the box. Place the letter in the blank 1.) _______: divides an angle into two congruent adjacent angles 2.) _______: equidistant from the endpoints of a segment, gives two equal pieces of the segment 3.) _______: something is congruent to itself 4.) _______: If two things are congruent to the same thing, then they are congruent. 5.) _______: intersects a segment at its midpoint and forms right angles 6.) _______: angles inside the parallel lines on opposite sides of the transversal 7.) _______: two pairs of corresponding sides and the angle between them are congruent 8.) _______: angles opposite each other when two lines cross 9.) _______: two pairs of corresponding angles and the side next to one of the corresponding angles are congruent 11.) ______: lines that intersect at right angles 12.) ______: two pairs of corresponding angles and the side between them are congruent 13.) ______: triangle with two congruent sides and its base angles are congruent 14.) ______: corresponding sides of two triangles are congruent 15.) ______: divide into two congruent pieces 16.) ______: Angles on the same location of the parallel lines 17.) ______: pieces of congruent triangles are congruent, used after two triangles are proven congruent 18.) ______: change a congruent symbol of a statement to an equal sign or an equal sign to a congruent symbol a.SSS b. angle bisector f. AAS g. ASA c. midpoint d. SAS e. vertical angles h. corresponding parts of congruent triangles are congruent (CPCTC) k. perpendicular bisector l. bisect m. definition of congruence n. reflexive property o. alternate interior p. alternate exterior q. triangle sum r. same side interior s. corresponding angles t. isosceles triangle u. perpendicular lines v. parallel lines w. transitive property 35 Hints to congruency proofs: 1.) If parallel lines are given: look for a __________________________ and find ___________________ 2.) If the triangles share a side: it is ______________________ to itself by the ____________________ ________________________ 3.) If the triangles share a vertex: look for _________________ 4.) Must fit one of the four congruence criteria: __________, __________, _____________, or ____________. The parts needed must be proven ___________________ in the proof. 5.) ________________ or bisect: two ________________________ pieces Introduction to Congruency Proofs: Write a two column proof: 1.)Given: ππ β ππ , < πππ β < π ππ Prove: βπππ β βπ ππ 2.) Given: πΏπ β ππ, πΏπ β ππ, N is the midpoint of MO Prove: βππΏπ β βπππ Filling in a Congruency Proof: Fill in the missing statements and reasons 3.) Given: BA is the perpendicular bisector of RT Prove: βRBA β βTBA Statements Reasons 1.) 1.) 2.)m<ABT=90; m<ABR=90 2.) 3.) 3.)Transitive Property 4.) < π΄π΅π β < π΄π΅π 4.) 5.) 5.) Def of perpendicular bisector 6.) π΅π΄ β π΅π΄ 6.) 7.) 7.) 36 4.) Given: AB ll CD, DB bisects AC Prove: πΈπ· β πΈπ΅ Statements Reasons 1.) AB ll CD, DB bisects AC 1.) 2.) 2.) Alternate interior angles 3.) AE β CE 3.) 4.) < π΄πΈπ΅ β < πΆπΈπ· 4.) 5.) βAEB β βCED 5.) 6.) πΈπ· β πΈπ΅ 6.) 37 Independent practice Lesson 17 W 1.) T Μ Μ Μ Μ ; ππ· Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ β₯ π·π Μ Μ Μ Μ β₯ ππ Given: ππ Prove: βπππ β βπ·ππ D S Statements Reasons 1.) 1.) Given 2.) < πππ β < π·ππ 2.) 3.) < π·ππ β < πππ 3.) Μ Μ Μ Μ β ππ Μ Μ Μ Μ 4.) ππ 4.) 5.) βπππ β βπ·ππ 5.) D A 2.) Given: X is the midpoint of BD X is the midpoint of AC X C B Prove: DA ο BC Statements Reasons 1. X is the midpoint of BD ; X is the midpoint of AC . 1. 2. 2. Definition of Midpoint 3. Μ Μ Μ Μ ππ· β Μ Μ Μ Μ ππ΅ 3. 4. < π·ππ΄ β < π΅ππΆ 4. 5 5. SAS Postulate 6. DA ο BC 6. 38