Proving Triangle Congruence and Circle Properties
This lesson explores triangle congruence proofs involving given conditions and common properties such as SAS (Side-Angle-Side) and CPCTC (Corresponding Parts of Congruent Triangles are Congruent). With an emphasis on understanding congruence in both triangles and circles, learners will enhance their geometric proof skills through structured reasoning. Key strategies include the Reflexive Property and recognizing congruent relationships between segments and angles. Students will be tasked with proving that certain segments are equal based on established geometric truths.
Proving Triangle Congruence and Circle Properties
E N D
Presentation Transcript
Warm up Given: SM Congruent PM <SMW Congruent <PMW Prove: SW Congruent WP • SM Congruent PM 1. Given • <SMW Congruent <PMW 2. Given • MW Congruent MW 3. Reflexive • ΔSMW Congruent ΔPMW 4. SAS • SW Congruent WF 5. CPCTC
WARM UP NW = SW Given <MNS = <TSN Given <3 = <4 Given <MNW = <TSW Subtraction <1 = < 2 Vertical <s are = Δ MNW = Δ TSW ASA MN = TS CPCTC
M P S W 3.3 CPCTC and Circles CPCTC: Corresponding Parts of Congruent Triangles are Congruent. Matching angles and sides of respective triangles.
M P S W Given: SM = PM <SMW = <PMWProve: SW = WP ~ ~ ~ • Statement Reason • SM = PM 1. Given • <SMW = <PMW 2. Given • MW = MW 3. Reflexive property • ΔSMW = ΔPMW 4. SAS (1, 2, 3) • SW = PW 5. CPCTC ~ ~ ~ ~ ~
• A • Circles: By definition, every point on a circle is equal distance from its center point. • The center is not an element of the circle. • The circle consists of only the rim. • A circle is named by its center. • Circle A or A •
Given: points A,B & C lie on Circle P.PA is a radiusPA, PB and PC are radii • Area of a circle Circumference • A = Лr2 C = 2Лr • We will usually leave in terms of pi • Pi = 3.14 or 22/7 for quick calculations • For accuracy, use the pi key on your calculator
T 19: All radii of a circle are congruent. Given: Circle O <T comp. <MOT <S comp. <POS Prove: MO = PO T P R K M O S ~
