Prove congruent angles have congruent supplements.
$begingroup$
Prove congruent angles have congruent supplements.
I do not yet have degrees.
Could I somehow use the base angles of isosceles triangles are congruent?
geometry euclidean-geometry
asked Feb 22 '15 at 17:50
user217443user217443
2913
$endgroup$
add a comment |
$begingroup$
Prove congruent angles have congruent supplements.
I do not yet have degrees.
Could I somehow use the base angles of isosceles triangles are congruent?
geometry euclidean-geometry
asked Feb 22 '15 at 17:50
user217443user217443
2913
$endgroup$
add a comment |
$begingroup$
Prove congruent angles have congruent supplements.
I do not yet have degrees.
Could I somehow use the base angles of isosceles triangles are congruent?
geometry euclidean-geometry
asked Feb 22 '15 at 17:50
user217443user217443
2913
$endgroup$
Prove congruent angles have congruent supplements.
I do not yet have degrees.
Could I somehow use the base angles of isosceles triangles are congruent?
geometry euclidean-geometry
geometry euclidean-geometry
asked Feb 22 '15 at 17:50
user217443user217443
2913
asked Feb 22 '15 at 17:50
user217443user217443
2913
asked Feb 22 '15 at 17:50
user217443user217443
2913
asked Feb 22 '15 at 17:50
user217443user217443
2913
asked Feb 22 '15 at 17:50
user217443user217443
2913
2913
add a comment |
add a comment |
1 Answer
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$begingroup$
Let $angle$BAC $cong$ $angle$EDF where AB $cong$ DE and AC $cong$ DF. We then have congruent triangles ABC and DEF by connecting B to C and E to F (they are congruent due to side-angle-side). Extend BA to a point P, and extend ED to a point Q such that AP $cong$ DQ. Then PBC $cong$ QEF (again using side-angle-side), meaining $angle$APC $cong$ $angle$DQF. Since AC $cong$ DF and PC $cong$ QF, APC $cong$ DQF so that $angle$PAC $cong$ $angle$QDF, which is the desired result.
answered Feb 22 '15 at 19:52
Tim ClarkTim Clark
34827
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1 Answer
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1 Answer
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$begingroup$
Let $angle$BAC $cong$ $angle$EDF where AB $cong$ DE and AC $cong$ DF. We then have congruent triangles ABC and DEF by connecting B to C and E to F (they are congruent due to side-angle-side). Extend BA to a point P, and extend ED to a point Q such that AP $cong$ DQ. Then PBC $cong$ QEF (again using side-angle-side), meaining $angle$APC $cong$ $angle$DQF. Since AC $cong$ DF and PC $cong$ QF, APC $cong$ DQF so that $angle$PAC $cong$ $angle$QDF, which is the desired result.
answered Feb 22 '15 at 19:52
Tim ClarkTim Clark
34827
$endgroup$
add a comment |
$begingroup$
Let $angle$BAC $cong$ $angle$EDF where AB $cong$ DE and AC $cong$ DF. We then have congruent triangles ABC and DEF by connecting B to C and E to F (they are congruent due to side-angle-side). Extend BA to a point P, and extend ED to a point Q such that AP $cong$ DQ. Then PBC $cong$ QEF (again using side-angle-side), meaining $angle$APC $cong$ $angle$DQF. Since AC $cong$ DF and PC $cong$ QF, APC $cong$ DQF so that $angle$PAC $cong$ $angle$QDF, which is the desired result.
answered Feb 22 '15 at 19:52
Tim ClarkTim Clark
34827
$endgroup$
add a comment |
$begingroup$
Let $angle$BAC $cong$ $angle$EDF where AB $cong$ DE and AC $cong$ DF. We then have congruent triangles ABC and DEF by connecting B to C and E to F (they are congruent due to side-angle-side). Extend BA to a point P, and extend ED to a point Q such that AP $cong$ DQ. Then PBC $cong$ QEF (again using side-angle-side), meaining $angle$APC $cong$ $angle$DQF. Since AC $cong$ DF and PC $cong$ QF, APC $cong$ DQF so that $angle$PAC $cong$ $angle$QDF, which is the desired result.
answered Feb 22 '15 at 19:52
Tim ClarkTim Clark
34827
$endgroup$
Let $angle$BAC $cong$ $angle$EDF where AB $cong$ DE and AC $cong$ DF. We then have congruent triangles ABC and DEF by connecting B to C and E to F (they are congruent due to side-angle-side). Extend BA to a point P, and extend ED to a point Q such that AP $cong$ DQ. Then PBC $cong$ QEF (again using side-angle-side), meaining $angle$APC $cong$ $angle$DQF. Since AC $cong$ DF and PC $cong$ QF, APC $cong$ DQF so that $angle$PAC $cong$ $angle$QDF, which is the desired result.
answered Feb 22 '15 at 19:52
Tim ClarkTim Clark
34827
edited Feb 22 '15 at 20:34
answered Feb 22 '15 at 19:52
Tim ClarkTim Clark
34827
answered Feb 22 '15 at 19:52
Tim ClarkTim Clark
34827
answered Feb 22 '15 at 19:52
Tim ClarkTim Clark
34827
34827
add a comment |
add a comment |
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