Problems on Right angle Triangles - Test Questions-i

Question 21

Question:   In the adjoining figure, m and n are two plane mirrors perpendicular to each other. Show that the incident ray CA is parallel to the reflected ray BD.

Answer:   
m and n are mirrors placed perpendicular to each other.





Similarly,


In right angled triangle BOA,



Multiplying by 2, we get

From (i) and (ii),

Question 22

Question:  

Answer:   






Adding (i) and (ii)

Question 23

Question:   In the adjoining figure, l || m and p || q. Show that and are supplementary.

Answer:   
l || m and p || q



l || m
...(i) ( corresponding angles)
p || q

...(ii) (Interior angles are supplementary)
From (i) and (ii) we have,

Question 24

Question:  

Answer:   




AE||BF






But these are alternate angles
AE||BF.

Question 25

Question:  

Answer:    ( sum of angles around a point)

Question 26

Question:   If lines AB, AC, AD and AE are parallel to a line l. What can be said about the points A, B, C, D and E?

Answer:   

AB, AC, AD, AE are parallel to l

l is a line, A is a fixed point not on the line l.
According to parallel axiom there is only one line through A which is parallel to l.
A, B, C, D and E are collinear points.

Question 27

Question:   In the adjoining figure, rays OA, OB, OC, OD and OE have the common point O. Show that
.

Answer:   
OA, OB, OC, OD, OE are rays with the common end point O.










By adding (i) and (ii), we get