Identify the postulate that proves the triangles are congruent.
sss
hl
asa
sas

D. HL (hypotenuse leg)

Step-by-step explanation:

There are two triangles in the picture, ABQ and CDP. The condition for the hypotenuse leg are:

1. both triangles are right triangle

2. the hypotenuse and one of the leg/side is equal

Both B and D angle is 90 degrees, so both triangles is right triangle. The hypotenuse for the triangle is AQ and PC, and both are equal. One of the triangles legs also equal, which is AB and CD. With that, you fulfill HL postulate for the congruent triangle.

Don't confuse this with SAS theorem for the same angle should be on the middle of two equal sides.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

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