If AABC is an equilateral triangle, then the mZA= 60°.
Choose the equivalent statement.

A. If AABC is not an equilateral triangle, then the mzA does not
equal 60°

B. If the mzA does not equal 60°, then AABC is not an equilateral
triangle.

C. If the m A = 60°, then AABC is an equilateral triangle.
=
I need help plz

In the following figure ΔABC is an equilateral triangle. Bisector of ∠B intersects circumcircle of ΔABC in point P. Prove that: CQ=CA

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Medium

Given: ΔABC is an equilateral triangle.

BP is the bisector of ∠B.

To Prove : CQ = CA

Proof : ΔABC is an equilateral Δ (Given)

∠ABC=∠CAB=∠ACB=60

o

(Given)

∠ABP=∠CBP (BP is the bisector)

∠CBP=

2

1

×∠ABC

∠CBP=

2

1

×60

o

=30

o

∠CBP=∠CAP=30

o

..... (1) (∠s incircled in the same arc)

∠ACB=60

o

(Given)

∴∠ACQ=180

o

−60

o

=120

o

(Linear pair)

∴∠ACQ=120

o

..... (2)

In ΔACQ,

∴∠AQC=180

o

−(30

o

+120

o

) From (1) and (2)

∠AQC=180

o

−150

o

∴∠AQC=30

o

...... (3)

In ΔACQ, ∠CAQ=∠AQC=30

o

From (1) and (3)

∴CQ=CA (Converse of isosceles Δ theorem)

3 years old and 8 years old

Step-by-step explanation:

8-3=5

3x8=24

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