A Weather Forecaster, predicts that their is a 50% chance of rain on Saturday and a 40% chance of rain on Sunday. If these proba
1 answer:
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Answer:
The completed two column proof is presented as follows;
Statement Reason
1. AC bisects ∠A and ∠C 1. Given
2. ∠ACB ≅ ∠ACD 2. Definition of bisector
3. ∠BAC ≅ ∠DAC 3. Definition of bisector
4. =
4. Reflexive PE
5. ≅
5. Segments with equal lengths are congruent
6. ΔABC ≅ ΔADC 6. By ASA
Step-by-step explanation:
The completed two column proof is presented as follows;
Statement
1. AC bisects ∠A and ∠C; The given data on the figure
2. ∠ACB ≅ ∠ACD; A bisected angle is divided into two equal angles which are congruent to each other
3. ∠BAC ≅ ∠DAC 3. Definition of bisector
4. =
4. Reflexive Property of Equality (PE)
5. ≅
5. Segments with equal lengths are congruent
6. ΔABC ≅ ΔADC 6. By Angle-Side-Angle, ASA, is a condition for congruency of two triangles
Where two angles and the included side between the two angles on one triangle are equal to two angles and the included side between the two angles on another triangle, the two triangles are said to be congruent by the Angle-Side-Angle ASA rule and therefore, they each have equal measures for all corresponding angles sides.
Answer:
Length of BE is
Step-by-step explanation:
The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. we have to find the length of the segment determined by the points of intersection between the line and the other two sides of the triangle.
Now, the two parts of triangle have equal area ∴ ar(ADE)=ar(BDEC)
⇒
⇒
In ΔABE and ΔABC,
∠A=∠A (Common)
∠ABE=∠ABC (Corresponding angles)
By AA similarity, ΔABE is similar to ΔABC.
Hence by area side proportionality theorem
⇒
⇒
⇒ units
Hence, length of BE is
