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1 Name Geometry Period ONE Ticket In Date Ticket In the Door! After watching the assigned video and learning how to construct a perpendicular line through a point, you will perform this construction below to demonstrate your mastery of this skill. 1. Using a compass and a straightedge, construct line m perpendicular to the given line through Potnt P. Leave all construction marks in your final answer. p 2. Fill in the blanks: I now the line that I constructed is perpendicular to the given line because it creates w this because it is similar to constructing a how to do. angles which I already know

2 Name Geometry Period 2-4 Notes Date Lesson 2-4: Constructing Altitudes and Squares (using side length) Today's Goal: How do I construct altitude and a square (given a side length)? Explain each step you took to complete your construction Construct the line perpendicular to AB through point p: 1. Place needle point on point P and swing the compass through segment AB so that it crosses the segment twice. 2. Label the two points of intersection, Q and R. 3. Construct a perpendicular bisector of segment QR. 4. The constructed line should pass through point P; p This is the line perpendicular to AB thorough point P Push Your Skills Construct any size right triangle DEF: How do the constructions on this page compare to the construction from your check in/video last night? sœvvo NJðL IIR-C

3 Before we construct! FACT CHECK: What is an altitude of a triangle? In Words Sketch a line that extends from of a triangle and is the side. Considering your sketch, what will the construction of an altitude require? L Yo BC rot va c Let's try this together: Construct an altitude in Triangle MNO label it MP Steps: 1. Place needle point on point and swing the compass through segment NO so that crosses the segment twice. O 2. Label the two points of intersection, A and B. 3. Construct a perpendicular bisector of segment AB. 4. The constructed line should pass through point M; this is th line perpendicular to BC thoro point x. 5. This is the altitude of the triangle.

4 List the properties of a square, With your shoulder partner, discuss how these properties can be used in the construction of a square. Properties of a Square Diagonals are perpendicular bisectors Adjacent sides are perpendicular Construction(s) that would lead to this property -Perpendicular Bisector Construction (Use when inscribed in a circle) 01 sides are congruent Construct a square given a side length 1) Watch me 2) Try on your own 3) Follow steps provided l. Extend line segment AB using a straightedge on side A, Z. Construct the perpendicular line at point A (just like yesterday's class) 3. Measure the distance from A to B with your compass. Needlepoint on A; swing arc above the line segment to mark distance of AB. Mark the intersection of this arc with the perpendicular line. Label D. (extend perpendicular line with straightedge if necessary) 5. Needlepoint on B; swing arc above the line segment to mark distance of AB. 6. Needlepoint point C; swing compass to cross at the arc made in step 5. Label the intersection C. 7. Draw segment CD and BC. Done!

5 LEYS Using only your compass and a straight edge, construct a square with side length XY: x YOU rag Using only your compass and a straight edge, construct a square with side length AB:

6 Name: Geometry PD. 2-4 Homework Date. plete each of the following problems. Check your work on the website when you're done 1) using a compass and a straightedge, construct the line that is perpendicular to the given line and passes through point p. 2) ON the line below, construct square MATH whose side length is equal to AB 4 3) The diagram below shows the construction of a line throug point P perpendicular to line m. Which statement is demonstrated by this construction? a) If a line is parallel to a line that is perpendicular to a third line, then the line is also perpendicular to the third line. p b The set of points equidistant from the endpoints of a line segment is the perpendicular bisector of the segment. Two lines are perpendicular if they are equidistant from a given point. 6) Two lines are perpendicular if they intersect to form a vertical line.

7 4) a) In the accompanying diagram of a construction, what type of special segment INSIDE a triangle, does PC represent? b) What is the relationship between PC and AB? c 5) Look at the construction of a square below. Identify two parts of the square and describe the specific constructions that you might be able to use to create a square. (For example, "side BC can be created with a straightedge." (This is just an example. Yours should be more involved]) c 6) In triangle PQR, using a compass, construct an altitude from vertex P to side QR.

8 Watch the assigned video and try your constructions on this page. Mastery of the ROOM content of this video is essential for our next lesson in class. Failure to watch the FLIPPED video will result in confusion and your inability to interact with your peers throughout ELASS the lesson. page bc checked cntraoçe ticket into to prove your mae,tcrv Of the concept, or a) What are we constructing in the video? I eo rac Ice: try it agajn' Try it again'