Question

2.6 - 2.7 practice
name:

1. are the following pairs of triangles congruent? if yes, create a congruence statement and name the congruence criteria sss, sas, asa, aas, hl.

a) yes / no
δ____ ≅ δ____
criteria ______
b) yes / no
δ____ ≅ δ____
criteria ______
c) yes / no
δ____ ≅ δ____
criteria ______
d) yes / no
δ____ ≅ δ____
criteria ______
e) yes / no
δ____ ≅ δ____
criteria ______

Explanation:

Step1: Analyze part a) triangles

Identify marked congruent sides: $DE=GE$, $\angle D=\angle G$, $CD=PG$. This matches SAS (two sides + included angle).

Step2: Analyze part b) triangles

Identify marked congruent sides: $AC=AP$, $CJ=PJ$, shared side $AJ$. This matches SSS (three sides).

Step3: Analyze part c) triangles

Identify marked congruent sides: $AB=AB$ (shared), $AO=BO$, $\angle CAB=\angle DBA$. This matches SAS (two sides + included angle).

Step4: Analyze part d) triangles

Identify marked congruent sides: $JK=JY$, $JT=JT$ (shared), $KT=YT$. This matches SSS (three sides).

Step5: Analyze part e) triangles

Identify right angles $\angle HAP=\angle MAP$, shared side $AP$, $HP=MP$. This matches HL (right triangle: hypotenuse + leg).

Answer:

a) Yes
$\Delta CDE \cong \Delta PGE$
Criteria: SAS

b) Yes
$\Delta ACJ \cong \Delta APJ$
Criteria: SSS

c) Yes
$\Delta ABC \cong \Delta BAD$
Criteria: SAS

d) Yes
$\Delta JKT \cong \Delta JYT$
Criteria: SSS

e) Yes
$\Delta HAP \cong \Delta MAP$
Criteria: HL