Answer: the answer is 4
Step-by-step explanation:
Prove: The segment joining the midpoints of two sides of a triangle is parallel to the third side.
1 answer:
Answer:
As per theorem Segment joining midpoints of two sides of a triangle is parallel to the third side.
Step-by-step explanation:
Given : In a triangle ABC, D and E are the midpoint of sides AB and AC.
To Proof : DE║BC
Construction: A line CF parallel to BA is drawn and De is extended to point F.
Proof : In a triangle ADE and EFC
Sides AD║CF and DF is transverse.Then ∠ADE = ∠CFE (Alternate angles)
Similarly AD║CF and AC is transverse then ∠DAE = ∠FCA (Alternate angles)
Therefore ΔADE≅ΔCEF (AAS property)
From this property side AD = Side CF (corresponding sides of the congruent triangles)
Therefore BD = CF
So sides BD and CF are equal and parallel to each other which represents DBCF is a parallelogram.
Therefore DE║BC
Hence proved.
You might be interested in
Answer:
Answer 1; Angles forming a linear sum to 180°
Answer 2; Substitution
Answer 3; Definition of perpendicular lines
Step-by-step explanation:
The two column proof is presented as follows;
Statement Reason
1. ∠SWT ≅ ∠TWU Given
2. m∠SWT + m∠TWU = 180° Angles forming a linear sum to 180°
3. m∠SWT + m∠SWT = 180° Substitution
4. m∠SWT = 90° Algebra
5. ⊥
Definition of perpendicular lines
Perpendicular lines are defined as lines that are at right angles (90°) to each other, therefore given that the angle formed by the lines and
m∠SWT = 90°, therefore, the lines
and
are perpendicular to each other.