Bridgette had a whole pie. She ate 1/4 of the pie for a snack and ate another 25% of the pie for dessert. What fraction of the p
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Which of the following conjectures is false?
Solution: The false conjecture is:
J. The sum of two odd numbers is odd
Explanation:
F. The product of two even numbers is even.
For example: Let us take two even numbers 4 and 6.
The product of two even numbers is:
Therefore, the product is also even number. Hence the conjecture is true.
G. The sum of two even numbers is even.
For example: Let us take two even numbers 4 and 6.
The sum of two even numbers is:
Therefore, the sum is also even number. Hence the conjecture is true.
H. The product of two odd numbers is odd.
For example: Let us take two odd numbers 3 and 5.
The product of two odd numbers is:
Therefore, the product is also odd number. Hence the conjecture is true.
J. The sum of two odd numbers is odd.
For example: Let us take two odd numbers 3 and 5.
The sum of two odd numbers is:
Therefore, the sum is not an odd number. Hence the conjecture is false.
Answer:
Step-by-step explanation:
<em><u>Given</u></em><u>:</u> A line m is perpendicular to the angle bisector of ∠A. We call this
intersecting point as D. Hence, in figure ∠ADM=∠ADN =90°.
AD is angle bisector of ∠A. Hence, ∠MAD=∠NAD.
<u><em>To Prove</em></u>: <em><u>ΔAMN is an isosceles triangle. i.e any two sides in ΔAMN are</u></em>
<em> </em><em><u>equal. </u></em>
<em><u>Solution</u></em>: Now, In ΔADM and ΔADN
∠MAD=∠NAD ...(1) (∵Given)
AD=AD ...(2) (∵common side)
∠ADM=∠ADN ...(3) (∵Given)
<u><em> Hence, from equation (1),(2),(3) ΔADM ≅ ΔADN</em></u>
( ∵ ASA congruence rule)
⇒<u><em> AM=AN</em></u>
Now, In Δ AMN
AM=AN (∵ Proved)
Hence, ΔAMN is an isosceles triangle.
