Geometry 5.5 SSS & HL Congruence & Proofs

• ∠B≇∠E and ∠C≇∠F
• ∠C≇∠F and AC≇DF
• ∠B≇∠E and AC≇DF
• ∠B≇∠E and ∠C≇∠F and AC≇DF

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

• ΔABC≅ΔBED by SAS
• ΔABC≅ΔBED by SSS
• ΔACB≅ΔDEB by SAS
• ΔACB≅ΔDEB by SSS

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

• Congruent by ASA
• Congruent by SAS
• Congruent by SSS
• Not Necessarily Congruent

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

• ΔABC≅ΔDCB by HL
• ΔABC≅ΔDCB by SAS
• ΔABC≅ΔDCB by SSA
• ΔABC≅ΔDCB by SSS

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

• ΔPQT≅ΔSRT by HL
• ΔPQT≅ΔSRT by SAS
• ΔPQT≅ΔSRT by SSA
• ΔPQT≅ΔSRT by SSS

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

• Congruent by ASA
• Congruent by SAS
• Congruent by SSS
• Not Necessarily Congruent

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

• DF≅FD by Reflexive Property so ΔDEF≅ΔDGF by SSS
• ∠E≅∠G are Vertical Angles so     ΔDEF≅ΔDGF by SSS
• DF≅FD by Symmetric Property so ΔDEF≅ΔDGF by SSS
• ∠E≅∠G are Alternate Interior Angles so ΔDEF≅ΔDGF by SSS

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

• Congruent by HL
• Congruent by SAS
• Congruent by SSS
• Not Necessarily Congruent

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

• Only PS≅RS because QS≅QS by Reflexive Property
• Only QS≅QS because PS≅RS by Reflexive Property
• Both QS≅QS and PR≅RS
• Both QS≅QS and PS≅RS

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.10

CCSS.HSG.SRT.B.5

• ΔLMN≅ΔSTU by HL
• ΔLMN≅ΔSTU by SAS
• ΔLMN≅ΔSTU by SSA
• ΔLMN≅ΔSTU by SSS

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8