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In this lesson, we will learn how to construct angle bisectors and perpendiculars from points outside straight lines.

Q1:

What does the following figure illustrate?

Q2:

Draw any line segment from a point π΅ to a point πΆ and bisect it at the point π· . From π· , draw a line perpendicular to π΅ πΆ to a point π΄ . What can you say about the lengths of π΄ π΅ and π΄ πΆ ?

Q3:

Q4:

What construction is illustrated below?

Q5:

Draw a triangle π΄ π΅ πΆ in which π΄ π΅ = 3 c m , π΅ πΆ = 4 c m , and π΄ πΆ = 5 c m . Bisect β π΅ with a line that intersects π΄ πΆ at the point π· . Measure the length of π΅ π· .

Q6:

Draw a triangle π΄ π΅ πΆ in which π΄ π΅ = π΄ πΆ = 1 2 c m and π΅ πΆ = 1 5 c m . First, bisect π΄ π΅ at π· and π΄ πΆ at πΈ , then connect the points to draw π· πΈ . Using the drawing, determine the length of π· πΈ

Q7:

Draw the triangle π΄ π΅ πΆ , where π΄ π΅ = 6 . 2 c m , π΅ πΆ = 1 2 c m , and π΄ πΆ = 1 3 c m . Then draw a perpendicular line from π΄ to π΅ πΆ intersecting it at π , and a perpendicular line from π΅ to π΄ πΆ intersecting it at π . Use the ruler to find the lengths of π΄ π and π΅ π .

Q8:

Draw a triangle π΄ π΅ πΆ , in which π΄ π΅ = 8 c m , π΅ πΆ = 6 c m , and π β π΅ = 1 2 0 β . Then draw a perpendicular line from π΄ to β ο© ο© ο© ο© β π΅ πΆ that intersects it at π , draw another perpendicular line from π΅ to β ο© ο© ο© ο© β π΄ πΆ that intersects it at π , and finally draw a perpendicular line from πΆ to β ο© ο© ο© ο© β π΄ π΅ that intersects it at π . Use the ruler to find the lengths of π΄ π , π΅ π , and πΆ π .

Q9:

Q10:

Q11:

Q12:

Draw the triangle π΄ π΅ πΆ , where π΄ π΅ = 5 . 8 c m , π΅ πΆ = 1 5 c m , and π΄ πΆ = 1 6 c m . Then draw a perpendicular line from π΄ to π΅ πΆ intersecting it at π , and a perpendicular line from π΅ to π΄ πΆ intersecting it at π . Use the ruler to find the lengths of π΄ π and π΅ π .

Q13:

Draw a triangle π΄ π΅ πΆ , in which π΄ π΅ = 5 c m , π΅ πΆ = 7 c m , and π β π΅ = 1 2 0 β . Then draw a perpendicular line from π΄ to β ο© ο© ο© ο© β π΅ πΆ that intersects it at π , draw another perpendicular line from π΅ to β ο© ο© ο© ο© β π΄ πΆ that intersects it at π , and finally draw a perpendicular line from πΆ to β ο© ο© ο© ο© β π΄ π΅ that intersects it at π . Use the ruler to find the lengths of π΄ π , π΅ π , and πΆ π .

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