15. Evaluate the expression 13 ÷ (2.5-1-3).33.
1 answer:
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Answer: Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.
Step-by-step explanation:
Given : ABCD is a parallelogram.
That is, AB ║ CD and AD ║BC
We have to prove that: AB≅CD and AD≅BC
Proof:
Construct diagonal AC in the parallelogram ABCD.
Since, AC ≅ AC ( reflexive)
∠ BAC ≅ ∠ DCA ( By the alternative interior angle theorem)
∠ BCA ≅ ∠ DAC ( By the alternative interior angle theorem)
⇒ Δ BCA ≅ Δ DAC ( By ASA congruence postulate )
⇒ AB≅CD as well as AD≅BC ( BY CPCTC )
Thus, the opposite side of the parallelogram are congruent.
Solution:
As we know reference angle is smallest angle between terminal side and X axis.
As cosine 45 ° is always positive in first and fourth quadrant.
i.e CosФ, Cos (-Ф) or Cos(2π - Ф) have same value.
As, Cos 45°, Cos (-45°) or Cos ( 360° - 45°)= Cos 315°are same.
So, Angles that share the same Cosine value as Cos 45° have same terminal sides will be in Quadrant IV having value Either Cos (-45°) or Cos (315°).
Also, Cos 45° = Sin 45° or Sin 135° i.e terminal side in first Quadrant or second Quadrant.
