Construct triangle xyz in which xy = 7 cm, yz = 4.5 cm, and xz = 3 cm. Draw a perpendicular line from point z to meet xy. What is the length of line zw?
Answer (2)
To construct triangle XYZ with given side lengths XY = 7 cm, YZ = 4.5 cm, and XZ = 3 cm, and to find the length of the perpendicular line ZW from Z to XY, follow these steps:
Draw the Base Line XY : Start by drawing a horizontal line segment XY that is 7 cm long.
Construct Arc for YZ : From point Y, use a compass to draw an arc with a radius of 4.5 cm. This will represent all potential positions for point Z.
Construct Arc for XZ : Similarly, from point X, draw another arc with a radius of 3 cm. The intersection point of the two arcs will be point Z.
Identify Point Z : Mark the intersection of the arcs as point Z.
Draw Triangle XYZ : Connect points X, Y, and Z to form triangle XYZ.
Draw Perpendicular ZW from Z : To find the length of the perpendicular line ZW, use a compass and straightedge:
From point Z, draw a vertical line that meets XY at point W, ensuring it forms a right angle (90 degrees) with the line XY.
Measure Line ZW : Use a ruler to measure the distance from Z to W along the perpendicular line you have drawn.
Solution of ZW : Since this is a basic construction using the properties of triangles, measurements can vary slightly depending on construction precision. If needed, use geometric calculations or triangle properties such as the Pythagorean theorem in case of right triangles to confirm the length of ZW.
This detailed construction approach allows you to graphically solve for ZW based on the unique properties of the triangle XYZ. Each step utilizes principles of geometry to accurately identify relationships between points and lines.
To construct triangle XYZ with the given side lengths, draw a horizontal line segment XY, and find point Z using arcs from X and Y. Next, draw the perpendicular line ZW from point Z to line XY and measure the length. The length of ZW is determined during the construction process, ensuring it's accurately formed right-angled to line XY.
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