Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Integer triangle wikipedia , lookup
Noether's theorem wikipedia , lookup
Rational trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
History of trigonometry wikipedia , lookup
Four color theorem wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
The Amazing Section 2.4 Congruent Supplements and Complements By: The amazing Jen Burke and the average Kathleen Shedlock (Gimpy) Supplementary Angles Two angles, whose sum is one hundred and eighty degrees. 70° J K 110° 70° 110° 180° Theorem 4 If angles are supplementary to the same angle, then they are congruent. C T 65° 65° A 115° Short Form: suppl of the same angle are congruent Sample Problem Given: <ACS suppl. <SCT S <ACS suppl. <STC Prove: <SCT is congruent to <STC Statements A C T Reasons 1. <ACS suppl <SCT 1. Given 2. <ACS suppl. 2. Given <STC 3. Suppl of the same 3. <SCT is congruent < are to <STC congruent Theorem 5 If angles are supplementary to congruent angles, then they are congruent. F R 45° 135° 135° 45° Short Form: suppls of congruent <s are congruent O G Sample Problem Given: <J suppl <B <K suppl <S <B <S Prove: <J <K Statements 1. <J suppl <B 2. <K suppl <S B J K S 3. <B <S 4. <J <K Reasons 1. Given 2. Given 3. Given 4. Suppl of <s are Complementary Angles • Two angles, whose sum is ninety degrees. A B 25° 65° 90° C Theorem 6 If angles are complementary to the same angle, then they are congruent. W 75° O 75° C 15° Short Form: Compls of the same < are Sample Problem Given: <DIC compl <DSI <CIS compl <DSI Prove: <CIS <DIC D C Statements Reasons 1. <DIC compl <DSI 1. Given 2. <CIS compl <DSI I S 2. Given 3. Compl of the same < are 3. <CIS <DIC Theorem 7 •If angles are complementary to congruent angles, then they are congruent. Short Form: compls of <s are I L 65° 25° 25° E F 65° Sample Problem 1 Statements Reasons 1. <1 compl <2 1. Given 2. <3 compl <4 2. Given 3. <4 <1 3. Given 4. <3 <2 4. Compls of <s are 2 3 4 Given: <1 compl <2 <3 compl <4, <4 <1 Prove: <3 <2 Practice Problem #1 A Given: BC DE ACB ADE Prove: BAD EAC Statements B C D E Reasons Answer to previous slide Statements Reasons 1. BC DE 1. Given 2. ACB ADE 2. Given 3. BD CE 3. Addition 4. ADE suppl ADC ACB suppl ACD 4. If two adj <s form a st <. They are suppl 5. ADC ACD 5. Suppls of <s are 6.ACDisos 6. If 2 base <s of a are that isos 7. AC AD 7. If isos then legs 8. BAD EAC 8. SAS (3,5,7) Practice Problem #2 V K O Given: O is the midpt of VP and TK OPT compl TOP OTP compl TOP VO KO Prove: VPT KTP Statements T P Reasons Answer to previous slide Statements Reasons 1.O mdpt of VP , TK 1. Given 2. OTP compl TOP OPT compl TOP 3. OTP OPT 2. Given 4. TP TP 5.VO KO 6. VP KT 7.VPT KTP 3. Compl of the same < are 4. Reflexive 5. Given 6. Multiplication 7. SAS (3,4,6) Works Cited "Isoscels Triangle Proof Example." Interactive Math Activities, Demonstrations, Lessons with Definitions and Examples, Worksheets, Interactive Activities and Other Resources. Web. 20 Jan. 2011. West Irondequoit Central School District. Web. 20 Jan. 2011. <http://www.westirondequoit.org>. Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, IL: McDougal, Littell, 1991. Print.