Geometric Representation Question

Based on the angles and sides on the triangles, all pairs of triangles can be similar or congruent. I explain both below as they willl be used for your other questions too:

Congruent is a mathematical term used to describe two figures or shapes that have the same size and shape. 

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Two triangles are similar if they have the same shape but not necessarily the same size. The corresponding angles are equal, and the corresponding sides are proportional.


First picture (from left):

Triangles are similar and we use proportions with similar triangles.

$\frac{8}{12} =\frac{16}{24}=\frac{23}{x}$

$x=34.5$


Second picture:

Triangles are similar (equal) and we use proportions with similar triangles.

$\frac{y}{6.4} =\frac{5.2}{5.2}$

$y=6.4$


Third picture:

Triangles are similar (equal) and we use proportions with similar triangles.

All sides are equal. The angle between two sides should be equal.

So:

The angle between sides 150 and 150 should be equal.

$z=40$