Consider the reflection of ΔABC across the line of reflection, Line P T.
2 right triangles are shown. Line P T is the line of reflection. Line segment A prime A has a midpoint at point S. Line segment B prime B has a midpoint at point R. Line segment C prime C has a midpoint at point Q.
Which statements must be true? Check all that apply.
A'A = C'C
C'Q = QC
Line P T⊥ A'A
C'C ⊥ B'B
A'A || B'B
m∠TRB = 90°
Answers
Answer:
True statements are B , C , E , F
Step-by-step explanation:
As per the question
we have given
- 2 right triangles
- Line P T is the line of reflection
- Line segment A prime A has a midpoint at point S.
- Line segment B prime B has a midpoint at point R.
- Line segment C prime C has a midpoint at point Q.
We have to tell which statements are true
As we know
Mid-Point Theorem Proof
If a line segment adjoins the mid-point of any two sides of a triangle, then the line segment is said to be parallel to the remaining third side and its measure will be half of the third side.
The converse of the midpoint theorem states that ” if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”.
∴ True statements are :
B) C'Q=QC
C) PT⊥A'A with the line on top
E) A'A|| B'B
F) m∠TRB = 90°
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Answer:
True statements are:
B) C'Q = QC
C) PT⊥A'A with the line on top
E) A'A || B'B
F) m∠TRB = 90°
Step-by-step explanation:
From the above question,
The reflection of ΔABC across the line of reflection, Line P T.
Two right triangles are shown. Line P T is the line of reflection. Line segment A prime A has a midpoint at point S. Line segment B prime B has a midpoint at point R.
Line segment C prime C has a midpoint at point Q.
They have given :
Line P T is the line of reflection
Line segment A prime A has a midpoint at point S.
Line segment B prime B has a midpoint at point R.
Line segment C prime C has a midpoint at point Q.
We have to tell which statements are true
Mid-Point Theorem Proof
If a line segment is parallel to the remaining third side of a triangle and its measure is half of the third side, then it adjoins the mid-point of any two sides of the triangle.
The midpoint theorem states that "if a line is drawn connecting the midpoints of two sides of a triangle, then it will divide the two sides proportionally and will be parallel to the third side".
True statements are:
B) C'Q = QC
C) PT⊥A'A with the line on top
E) A'A || B'B
F) m∠TRB = 90°
For more such related questions : https://brainly.in/question/17412895
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