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1. Supply the missing reasons to complete the proof:

Given: angle Q is congruent to angle T and line QR is congruent to line TR Prove: line PR is congruent to line SR


My answers:

1. Given
2. Vertical Angles
3. ASA
4. CPCTC

2. Complete the proof by providing the missing statement and reasons.

Given: SD-HT; SH=ST

Prove: SHD=STD

My answers:

1. Given
2. Definition Of Perpendicular Line
3. Given
4. SD=DS
5. HL theorem

1 Supply the missing reasons to complete the proof Given angle Q is congruent to angle T and line QR is congruent to line TR Prove line PR is congruent to line class=
1 Supply the missing reasons to complete the proof Given angle Q is congruent to angle T and line QR is congruent to line TR Prove line PR is congruent to line class=

Respuesta :

Answer:

(1) The triangle PQR and SRT are congruent by ASA postulate. The sides PR and SR are congruent by CPCTC.

(2) The angles SDH and SDT are right angles by definition of perpendicular line. SD=DS by reflexive property. Triangles SHD and STD are congruent by HL theorem.

Step-by-step explanation:

(1)

From the given information

[tex]\angle Q\cong \angle T[/tex]

[tex]QR\cong TR[/tex]

[tex]\angle PRQ\cong \angle SRT[/tex]       (Vertical angles are congruent)

By ASA postulate the triangles PRQ and SRT are congruent.

[tex]\triangle PRQ\cong \triangle \SRT[/tex]

According to CPCTC(corresponding parts of congruent triangles are congruent).

[tex]PR\cong SR[/tex]

Therefore, the triangle PQR and SRT are congruent by ASA postulate. The sides PR and SR are congruent by CPCTC.

(2)

Given Information: SD⊥HT

[tex]SH\cong ST[/tex]

According to the definition of perpendicular line, if a line intersects another line at right angle (90 degree), then the lines are perpendicular to each other.

Since the lines SD and HT are perpendicular lines therefore the angles between them is 90 degree.

The angle SDH and angle SDT are right angles.

[tex]\angle SDH\cong \angle SDT=90^{\circ}[/tex]      (Rights angles)

[tex]SH\cong ST[/tex]                                                    (Given)

[tex]SD\cong SD[/tex]                                                   (Common side)

[tex]SD\cong DS[/tex]                                                   (reflexive property)

If one leg and hypotenuse of two right angles are congruent, then these triangles are congruent to each other by HL postulate. So by HL theorem

[tex]\triangle SHD\cong \triangle \STD[/tex].

Ver imagen DelcieRiveria
Ver imagen DelcieRiveria
MrRoyal

Similar triangles may or may not be congruent.

  • The missing statements are: Congruent by ASA postulate and Congruent by CPCTC.
  • The missing statements are: Definition of perpendicular line, Given, Congruent by HL theorem and [tex]\mathbf{SD \cong DS}[/tex]

(a) Triangles PQR and TSR

From the question, we have:

[tex]\mathbf{\angle Q \cong \angle T}[/tex] , [tex]\mathbf{QR \cong TR}[/tex] and [tex]\mathbf{\angle PRQ \cong SRT}[/tex].

The above means that, 2 angles and 1 side lengths are congruent.

i.e. the triangles are congruent by ASA postulate.

Sides PR and SR are corresponding parts.

So, the next blank will be completed using: CPCTC

(b) Triangles SHD and STD

From the question, we have:

[tex]\mathbf{SD \perp HT}[/tex]

This means that, angles at D in both triangles are congruent by definition of perpendicular lines.

[tex]\mathbf{SD \cong HT}[/tex] is given

The distance SD is the same as distance DS,

So, SD = DS, by reflective property

Lastly, the triangles are Congruent by HL theorem

Read more about similar and congruent triangles at:

https://brainly.com/question/19589236

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