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Answers
Step-by-step explanation:
1. ∵∠ADC=∠DCA
∴AD=DC (Base angles of isoceles Δ are equal)
∵ ABCD Is a Rectangle
∴AB=CD, BC= AD
∵AD=DC
∴AB= BC =CD=DA
∵All angles of a rectangle are 90
∴ABCD is a square
2. Construct Diagonal BD
in a square all sides are equal
∴BC= CD
∴∠CDB=∠CBD - 1( Base angles of isoceles Δ are equal
similiarly in ΔBDA
∠ABD=∠ADB - 2
∵∠ABD= ∠CDB (alternate interior angles)
∴∠ABD= ∠CDB=∠ADB=∠CBD (from 1 and 2)
∴BD BISECTS ∠B and ∠D
∴
∴
Answer:
1. ∵∠ADC=∠DCA
∴AD=DC (Base angles of isoceles Δ are equal)
∵ ABCD Is a Rectangle
∴AB=CD, BC= AD
∵AD=DC
∴AB= BC =CD=DA
∵All angles of a rectangle are 90
∴ABCD is a square
2. Construct Diagonal BD
in a square all sides are equal
∴BC= CD
∴∠CDB=∠CBD - 1( Base angles of isoceles Δ are equal
similiarly in ΔBDA
∠ABD=∠ADB - 2
∵∠ABD= ∠CDB (alternate interior angles)
∴∠ABD= ∠CDB=∠ADB=∠CBD (from 1 and 2)
∴BD BISECTS ∠B and ∠D
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Step-by-step explanation: