document.write( "Question 758773: Given: ∠BAD ≈ ∠CAD
\n" ); document.write( "line AD perpendicular to line BC\r
\n" ); document.write( "\n" ); document.write( "Prove Triangle ABC is isosceles \n" ); document.write( "

Algebra.Com's Answer #461697 by MathLover1(20850) $\"\"$ $\"About$

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Since given that $\"AD\"$ is perpendicular to $\"BC\"$ => angle $\"ADC=90\"$ degrees and angle $\"ADB=90\"$ degrees,
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\n" ); document.write( "so angle $\"ADC\"$ is congruent to angle $\"ADB\"$
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\n" ); document.write( "The measure of angle $\"BAD\"$ is equal to $\"180\"$ minus $\"90\"$ minus the measure of angle $\"ADB\"$ , \r
\n" ); document.write( "\n" ); document.write( "but since the measure of $\"ADB=+ADC\"$ ,
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\n" ); document.write( "the measure of angle $\"BAD\"$ is equal to $\"180\"$ minus $\"90\"$ minus the measure of angle $\"ADC\"$
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\n" ); document.write( "However, that is exactly the measure of angle $\"CAD\"$ .
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\n" ); document.write( "Hence angle $\"BAD\"$ is congruent to angle $\"CAD\"$ .
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\n" ); document.write( "Since $\"AD+=+AD\"$ , triangle $\"ADC\"$ is congruent to triangle $\"ADB\"$ by $\"SAS\"$ . \r
\n" ); document.write( "\n" ); document.write( " Then $\"AB+=+AC\"$ by $\"CPCT\"$ , and finally $\"ABC\"$ is $\"isosceles\"$ by $\"definition\"$ .\r
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\n" ); document.write( "\n" ); document.write( "or:\r
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\n" ); document.write( "\n" ); document.write( "Given: AD perpendicular to BC; angle BAD congruent to CAD
\n" ); document.write( "Prove: ABC is isosceles\r
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\n" ); document.write( "\n" ); document.write( "Proof:
\n" ); document.write( "statement..........................................reason
\n" ); document.write( "1. angle $\"BAD\"$ congruent to angle $\"CAD\"$ ..........................given
\n" ); document.write( "2. $\"AD\"$ is perpendicular to $\"BC\"$ , => $\"BDA\"$ is congruent to the angle $\"CDA\"$ ..........all right angles are congruent
\n" ); document.write( "3. $\"AD\"$ is congruent to $\"AD\"$ .......................... reflexive property
\n" ); document.write( "4. triangle $\"BAD\"$ congruent to triangle $\"CAD\"$ ...........by SAS
\n" ); document.write( "5. $\"AB\"$ is congruent to $\"AC\"$ ...................corresponding parts of congruent triangles are congruent
\n" ); document.write( "6. triangle $\"ABC\"$ is isosceles ....................it has two congruent sides \r
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