Answer:
B.False
Step-by-step explanation:
We are given that two right angle are not similar and they have one congruent acute angle in common.
We have to tell the statement is false or true.
Suppose two right angles triangle ABC and EFG which are not similar
Let Angle B and angle F are of 90 degrees
One acute angle common in two triangles
Suppose that angle C=angle G=x, angle A=y, angle E=z
In right angled triangle ABC
[tex]m\angle A+m\angle B+m\angle C=180^{\circ}[/tex]
[tex]x+y+90=180^{\circ}[/tex]
In right angled triangle EFG
[tex]m\angle E+m\angle F+m\angle G=180^{\circ}[/tex]
[tex]z+x+90=180^{\circ}[/tex]
Substitute the values equal then we get
[tex]x+y+90=z+x+90[/tex]
[tex]x+y+90-x-90=z[/tex]
[tex]y=z[/tex]
Hence, all three angles of a right triangle are similar to all three corresponding angles of another right angled triangle.
Therefore, the two triangles must be similar by AAA similarity postulates.
Hence, the statement is false.
