Start with constructing a pair of perpendicular segments. Then, mark the points equidistant from their intersection using a compass.
Isosceles Right Triangle I
Isosceles Right Triangle II
Isosceles Right Triangle III
Practice makes perfect
To construct the isosceles right triangles, we will start with constructing a pair of perpendicular segments. Let's draw a segment using a ruler and choose several points on it.
Next, we will draw a segment that is perpendicular to XZ using a compass. We will first put the compass point on X and draw an arc.
With the same compass setting, we will put the compass point on point Y and draw another arc.
By drawing a segment which passes through the intersection points of the arcs, we will have the pair of perpendicular segments.
Next, we will mark the points equidistant from their intersection using the compass.
Let's connect these marks and draw the first isosceles right triangle.
Changing the setting of the compass, we can draw two more isosceles right triangles.
Isosceles Right Triangle I
Isosceles Right Triangle II
Isosceles Right Triangle III
By measuring the legs of each triangle, we can verify that AB=AC, DE=DF, and GH=GJ. We can also confirm that ∠ A, ∠ D, and ∠ G are right angles using a protractor.
