The vertices of triangle WXY have coordinates W(3,2)X(5,5)Y(7,3). Triangle WXY was transformed to produce triangle W'X'Y' with c
1 answer:
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<u>Answer with step-by-step explanation:</u>
We are given three different expressions and we are to write an equivalent exponential equation for them.
We know that the standard form of a logarithmic expression is given by:
which is equivalent to the exponential form
.
1. --->
2. --->
3. --->
Answer:
Given :- ABCD is a square.
To proof :- AC = BD and AC ⊥ BD
Proof :- In △ ADB and △ BCA
AD = BC [ Sides of a square are equal ]
∠BAD = ∠ABC [ 90° each ]
AB = BA [ Common side ]
△ADB ≅ △BCA [ SAS congruency rule ]
⇒ AC = BD [ Corresponding parts of congruent triangles are equal ]
In △AOB and △AOD
OB = OD [ Square is also a parallelogram therefore, diagonal of parallelogram bisect each other ]
AB = AD [ Sides of a square are equal ]
AO = AO [ Common side ]
△AOB ≅ △ AOD [ SSS congruency rule ]
⇒ ∠AOB = ∠AOD [ Corresponding parts of congruent triangles are equal]
∠AOB + ∠AOD = 180° [ Linear pair ]
∠ AOB = ∠AOD = 90°
⇒ AO ⊥ BD
⇒ AC ⊥ BD
Hence proved, AC = BD and AC ⊥BD
