Construct triangle ABC in which[AB]=10cm[BC]=6cm and ΔABC 45°
ii. locate the point D inside the triangle ABC such that D is equidistant through D to cut AB at x and AC at y such that Ax=AY
iv. Measure[AY]
To construct triangle ABC with given side lengths and angle measures, follow these steps:
i. Draw a line segment AB of length 10 cm. This will be the base of the triangle.
ii. From point A, use a protractor to draw a line segment AC at an angle of 45 degrees to AB. The length of AC will be determined in subsequent steps.
iii. Construct a perpendicular bisector of AB. To do this, use a compass to find the midpoint of AB (let's call it M). Set the compass width to a length greater than half of AB and draw two arcs centered at M, intersecting AB at two points.
iv. Connect the intersection points on AB to create a line segment perpendicular to AB.
v. Bisect the angle between AB and the perpendicular line segment using a compass. This will give you the line bisecting angle A of triangle ABC.
vi. Set the compass width to 6 cm (length of BC) and draw an arc with center B intersecting the bisecting line. Label the point of intersection as C.
vii. Connect the points A and C to complete triangle ABC.
Now, to locate point D inside triangle ABC such that it is equidistant from AB and AC, you can follow these steps:
i. Draw a line segment AX from point A that intersects AB. The length of AX can be any value, as long as it is not zero.
ii. From point A, use a compass to draw an arc with a radius equal to the length of AX.
iii. Similarly, draw an arc from point A with a radius equal to the length of AC.
iv. Let the points where the two arcs intersect be labeled as X and Y. Connect points X and Y to point D.
v. Point D will be the intersection of line segments XY and BC.
To measure the length AY, you can use a ruler:
i. Place the ruler or a measuring tape from point A to point Y, ensuring that it is straight and aligned with the line segment.
ii. Read the measurement on the ruler at the point where it intersects with point Y. This will give you the length of AY.