Chapter 5 Applying Congruent Triangles 5.1 Special Segments in
Triangles 5.1 Day 2 Proofs Warm Up For Chapter 5
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5.1 Special Segments in Triangles Objective: Identify and use
medians, altitudes, angle bisectors, and perpendicular bisectors in
a triangle How will I use this? Special segments are used in
triangles to solve problems involving engineering, sports and
physics. Click Me!! Median Perpendicular Bisector Altitude Chapter
5 Angle Bisector An example to tie it all together
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A segment that connects a vertex of a triangle to the midpoint
of the side opposite the vertex.
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A line segment with 1 endpoint at a vertex of a triangle and
the other on the line opposite that vertex so that the line segment
is perpendicular to the side of the triangle.
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Perpendicular Bisector: A line or line segment that passes
through the midpoint of a side of a triangle and is perpendicular
to that side. Perpendicular Bisector Theorems!
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Theorem 5.1: Any point on the perpendicular bisector of a
segment is equidistant from the endpoints of the segment. Theorem
5.2: Any point equidistant from the endpoints of a segment lies on
the perpendicular bisector of the segment. Theorems Median
Perpendicular Bisector Altitude Chapter 5 Angle Bisector
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Theorems Theorem 5.3: Any point on the bisector of an angle is
equidistant from the sides of the angle. Theorem 5.4: Any point on
or in the interior of an angle and equidistant from the sides of an
angle lies on the bisector of the angle. Median Perpendicular
Bisector Altitude Chapter 5 Angle Bisector
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Warm UP In Find the value of x and the measure of each
angle.
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Warm Up Answers How did I get that? Click the answer to see!
BONUS!!! What type of triangle is ABC? Click me to find the
Answer!! Section 5.1
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BONUS!!! What type of triangle is ABC? Click me to find the
Answer!!
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} Because the question give you angle measures, we take the sum
of the angles and set them equal to 180. Combine like terms! Add 20
to both sides! Divide by 10 on both sides! }} Chapter 5 Section 5.1
BONUS!! Click Me!!
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Use substitution for the answer you found for x and plug it
into the equation for angle A. Chapter 5 Section 5.1 BONUS!! Click
Me!!
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Use substitution for the answer you found for x and plug it
into the equation for angle B. Chapter 5 Section 5.1 BONUS!! Click
Me!!
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Use substitution for the answer you found for x and plug it
into the equation for angle C. Chapter 5 Section 5.1 BONUS!! Click
Me!!
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Triangle ABC is a right isosceles triangle Why is that??
Chapter 5 Section 5.1
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Angle Bisector What is an Angle Bisector? Click me to find out!
Move my vertices around and see what happens!! Angle Bisector
Theorems Section 5.1 Example
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Median Example Draw the three medians of triangle ABC. Name
each of them. A B C Answer
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Median Example Draw the three medians of triangle ABC. Name
each of them. A B C D E F Back to Section 5.1
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Altitude Example Draw the three altitudes, QU, SV, and RT. Q R
S Answer
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Altitude Example Draw the three altitudes, QU, SV, and RT. Q R
S U V T Back to Section 5.1
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Perpendicular Bisector Example Draw the three lines that are
perpendicular bisectors of XYZ. X Y Z Answer Label the lines l, m,
and n.
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Perpendicular Bisector Example Draw the three lines that are
perpendicular bisectors of XYZ. X Y Z l m n Back to Section
5.1
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Angle Bisector Example If BD bisects ABC, find the value of x
and the measure of AC. A B C D Answer
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Angle Bisector Example If BD bisects ABC, find the value of x
and the measure of AC. A B C D Show me how you got those answers!
Back to Section 5.1
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Angle Bisector Example If BD bisects ABC, find the value of x
and the measure of AC. A B C D Means that the angle is split into 2
congruent parts. Set the two angles equal to each other and solve.
Once you find x, plug it into AD and DC. Since you are looking for
the total length, AC, use segment addition to find the total
length. Back to Section 5.1
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5.1 Proofs Together YOU TRY!!!
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Given: Prove: 1 1 2 3 4 5 6 7 1. Given 2. Def of Isos Triangle
3. Def of Angle Bisector 4. Reflexive 5. SAS 6. CPCTC 7. Def of
Median 5.1 Proofs Just keep clicking!
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Given: Prove: 1 1 2 3 4 5 6 7 1. Given 2. Def of Equilateral
Triangle 3. Def of Angle Bisector 4. Reflexive 5. SAS 6. CPCTC 7.
Def of Median Just keep clicking! Were done, take me back to the
beginning!
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Example median Midpoint See the Work!! S G B Keep clicking to
see graph!
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What is the Midpoint Formula? Midpoint of GB Next Question Just
keep clicking!
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What can we conclude? Were done, take me back to the beginning!
Just keep clicking!
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5.2 Right Triangles An Internet Activity CLICK TO BEGIN
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Leg Theorem Leg Angle Theorem Hypotenuse Angle Theorem
Hypotenuse Leg Postulate Click on the triangle and learn about the
Theorems or Postulates. Click me when done Take notes as you read
along with each Theorem or Postulate!!
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Examples Solving for variables Stating additional information I
finished! Click me!!
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Solve for Example 1 Example 2 Example 3
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State the additional information. Example 1 Example 2 Example
3
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D EF P QR
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D E F P Q R
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D E F P Q R
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Back to Beginning
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State the additional information needed to prove the pair of
triangles congruent by LA. M J K L
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Proving triangles congruent by LA means a leg and an angle of
the right triangle must be congruent. M J K L OR Next Example
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State the additional information needed to prove the pair of
triangles congruent by HA. T S Z YX V
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State the additional information needed to prove the pair of
triangles congruent by HA. T S Z YX V The keyword was additional.
When proving triangles congruent by HA, all that is needed is to
show that the hypotenuse is congruent on each triangle as well as
an acute angle. In these triangles both are already shown so there
is no ADDITIONAL information needed. Next Example
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State the additional information needed to prove the pair of
triangles congruent by LA. D F C B A
