Given:
Two triangles are congruent, i.e.,
.
To find:
All the measures of both triangle.
Solution:
We have,
.
We know that, corresponding parts of congruent triangles are congruent (CPCTC).
![\angle A=\angle X](/tpl/images/0829/6300/d619c.png)
![\angle B=\angle Y=90^\circ](/tpl/images/0829/6300/b58ca.png)
![\angle C=\angle Z=37^\circ](/tpl/images/0829/6300/a70a8.png)
It triangle ABC,
(Angle sum property)
![\angle A+90^\circ+37^\circ=180^\circ](/tpl/images/0829/6300/be1f6.png)
![\angle A+127^\circ=180^\circ](/tpl/images/0829/6300/c5828.png)
![\angle A=180^\circ -127^\circ](/tpl/images/0829/6300/31920.png)
![\angle A=53^\circ](/tpl/images/0829/6300/734fc.png)
So,
![\angle A=\angle C=53^\circ](/tpl/images/0829/6300/17d15.png)
![AB=XY=3\text{ units}](/tpl/images/0829/6300/cc2de.png)
![BC=YZ=4\text{ units}](/tpl/images/0829/6300/79bcd.png)
![AC=XZ=5\text{ units}](/tpl/images/0829/6300/ff45b.png)
Therefore, m∠A = 53˚, m∠B =90˚
, m∠C =37˚
, m∠X = 53˚, m∠Y =90˚
, m∠Z =37˚
, Segment AB = 3 units
, Segment BC = 4 units
, Segment AC = 5 units
, Segment XY = 3 units
, Segment YZ = 4 units
, Segment XZ = 5 units
.