Question

The figure below shows a square ABCD and an equilateral triangle DPC:

ABCD is a square. P is a point inside the square. Straight lines join points A and P, B and P, D and P, and C and P. Triangle DPC is an equilateral triangle.

Ted makes the chart shown below to prove that triangle APD is congruent to triangle BPC:

Statements Justifications
In triangles APD and BPC; DP = PC Sides of equilateral triangle DPC are equal
In triangles APD and BPC; AD = BC Sides of square ABCD are equal
Angle ADC = angle BCD = 90° so angle ADP = angle BCP = 30°
Triangles APD and BPC are congruent SAS Postualte

Answer 1

here are the answer choices:

Which of the following completes Ted's proof?
In square ABCD; angle ADC = angle BCD
In square ABCD; angle ADP = angle BCP
In triangles APD and BPC; angle ADC = angle BCD
In triangles APD and BPC; angle ADP = angle BCP

Answer 2

@duckerstar146 @mathstudent55

Answer 3

Sorry, not to sure about this one, I just know for a fact that it's not B or C

Answer 4

My best bet, it probally D, is it includes the same order, and is actually similar triangles

Answer 5

ok, ill try that one

Answer 6

OKAY, i Have ONE more question

Answer 7

Look at the right triangle ABC:

Right triangle ABC has a right angle at B. Segment BD meets segment AC at a right angle.

A student made the following chart to prove that AB2 + BC2 = AC2:


Statement Justification
1. Triangle ABC is similar to triangle BDC 1. Angle ABC = Angle BCD and Angle BCA = Angle DBC
2. BC2 = AC • DC 2. BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC
3. Triangle ABC is similar to triangle ABD 3. Angle ABC = Angle ADB and Angle BAC = Angle BAD
4. AB2 = AC • AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ADB
5. AB2 + BC2 = AC • AD + AC • DC = AC (AD + DC) 5. Adding Statement 1 and Statement 2
6. AB2 + BC2 = AC2 6. AD + DC = AC

Which justification is incorrect?
Justification 4
Justification 1
Justification 2
Justification 3

Answer 8

@duckerstar146